SEMICONDUCTORS AND SEMIMETALS VOLUME 5
Infrared Detectors
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SEMICONDUCTORS AND SEMIMETALS VOLUME 5
Infrared Detectors
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SEMICONDUCTORS AND SEMIMETALS Edited by R. K . WILLARDSON BELL AND HOWELL ELECTRONIC MATERIALS DIVISION PASADENA, CALIFORNIA
ALBERT C. BEER BATTELLE MEMORIAL INSTITUTE COLUMBUS LABORATORIES COLUMBUS, OHIO
VOLUME 5 Infrared Detectors
1970
ACADEMIC PRESS New York and London
COPYRIGHT @ 1970, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED NO PART OF THIS B O O K MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, RETRIEVAL SYSTEM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.
ACADEMIC PRESS, INC. 1 1 1 Fifth Avenue, New York, New Y ork 10003
Uniied Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD Berkeley Square House, London Wl X 6BA
LIBRARY OF CONGRESS CATALOG CARDNUMBER: 65-26048
PRINTED IN THE UNITED STATES OF AMERICA
List of Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.
F. R. ARAMS, Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) T. C. HARMAN, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (1 11) R. J. KEYES,Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (32 1) PAULW. KRUSE,Honeywell Corporate Research Center, Hopkins, Minnesota (15) HENRYLEVINSTEIN, Physics Department, Syracuse University, Syracuse, New York (3) DONALD LONG,Honeywell Corporate Research Center, Hopkins, Minnesota (175) IVARSMELNGAILIS, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (1 11) F. P. PACE,Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) B. J. PEYTON, Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) M. B. PRINCE,' Electro-Optical Systems, Inc., A Xerox Company, Pasadena, California (85) E. H. PUTLEY, Ministry of Technology, Royal Radar Establishment, Malvern, Worcestershire, England (259) T. M. QUIST,Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (32 1) E. W. SARD,Airborne htruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409)
' Present address: Solid State Radiations, Inc., Los Angeles, California. V
vi
LIST OF CONTRIBUTORS
L. SCHMIT, Honeywell Corporate Research Center, Hopkins, Minnesota (1 75) ROBERTSEHR, Solid State Electronics Branch, McDonnell Douglas Astronautics Company, Western Division, Santa Monica, California (467) H . S. SOMMERS, JR., RCA Laboratories, David Sarnofl Research Center, Princeton, New Jersey (435) NORMAN B. STEVENS, Santa Barbara Research Center, Subsidiary of Hughes Aircraft Company, Santa Barbara, California (287) M. C. TEICH,Department of Electrical Engineering, Columbia University, New York, New York (361) RAINERZULEEG, Solid State Electronics Branch, McDonnell Douglas Astronautics Company, Western Division, Santa Monica, California (467) JOSEPH
Preface The extensive research that has been devoted to the physics of semiconductors and semimetals has been very effective in increasing our understanding of the physics of solids in general. This progress was made possible by significant advances in material preparation techniques. The availability of a large number of semiconductors with a wide variety of different and often unique properties enabled the investigators not only to discover new phenomena but to select optimum materials for definitive experimental and theoretical work. In a field growing at such a rapid rate, a sequence of books which provide an integrated treatment of the experimental techniques and theoretical developments is a necessity. The books must contain not only the essence of the published literature, but also a considerable amount of new material. The highly specialized nature of each topic makes it imperative that each chapter be written by an authority. For this reason the editors have obtained contributions from a number of such specialists to provide each volume with the required detail and completeness. Much of the information presented relates to basic contributions in the solid state field which will be of permanent value. While this sequence of volumes is primarily a reference work covering related major topics, certain chapters will also be useful in graduate study. In addition, a number of the articles concerned with applications of specific phenomena will be of value to workers in various specialized areas of device development. Because of the important contributions which have recently resulted from studies of the III-V compounds, the first few volumes of this series have been devoted to the physics of these materials: Volume 1 reviews key features of the III-V compounds, with special emphasis on band structure, magnetic field phenomena, and plasma effects. Volume 2 emphasizes physical properties, thermal phenomena, magnetic resonances, and photoelectric effects, as well as radiative recombination and stimulated emission. Volume 3 is concerned with optical properties, including lattice effects, intrinsic absorption, free carrier phenomena, and photoelectronic effects. Volume 4 includes thermodynamic properties, phase diagrams, diffusion, hardness, and phenomena in solid solutions as well as the effects of strong electric fields, hydrostatic pressure, nuclear irradiation, and nonuniformity of impurity
vii
Viii
PREFACE
distributions on the electrical and other properties of 111-V compounds. The present volume differs in scope from its predecessors in that, being devoted to infrared detectors, it becomes the first of a number of volumes to deal specifically with applications of semiconductor properties. Many chapters in the volume emphasize the exploitation of unique characteristics in certain materials; other chapters are concerned with special detection techniques. Because of time and space limitations, a number of articles had to be postponed for a later volume. In addition to further chapters on infrared detection, subsequent volumes of Semiconductors and Semimetals will be devoted to other applications such as high-temperature diodes and power rectifiers, field-effect transistors, IMPATT diodes, tunnel diodes, and applications of bulk negative resistance. Volumes will also deal with such fundamental phenomena as charge-carrier injection, lattice dynamics, galvanomagnetic effects, luminescence, and nonlinear optical phenomena. The editors are indebted to the many contributors and their employers who made this series possible. They wish to express their appreciation to the Bell and Howell Company and the Battelle Memorial Institute for providing the facilities and the environment necessary for such an endeavor. Thanks are also due to the U.S. Air Force Offices of Scientific Research and Aerospace Research and the U.S. Navy Office of Naval Research and the Corona Laboratories, whose support has enabled the editors to study many features of compound semiconductors. The assistance of Rosalind Drum, Martha Karl, and Inez Wheldon in handling the numerous details concerning the manuscripts and proofs is gratefully acknowledged. Finally, the editors wish to thank their wives for their patience and understanding. R. K. WILLARDSON ALBERTC. BEER
Contents . . . PREFACE . . . . . CONTENTS OF PREVIOUS VOLUMES . LISTOFCONTRIBUTORS
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v vii xiii
INTRODUCTION Chapter 1 Characterizationof Infrared Detectors
Henry Levinstein I. Introduction . . . . 11. Characterization of Detectors .
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111-V COMPOUNDS Chapter 2 Indium Antimonide Photoconductive and PhotoelectromagneticDetectors
Paul W. Kruse I. Introduction .
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11. Electrical Properties, Optical Properties, and Lifetime Values of Importance to
the Design of lnSb Infrared Detectors . . . . . 111. Theoretical Detector Design . . . . . . . IV. Preparation of Photoconductive and Photoelectromagnetic Detectors V. Performance of Photoconductive and Photoelectromagnetic Detectors
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Chapter 3 Narrowband Self-Filtering Detectors
M . B. Prince 1. Introduction . . 11. Theoretical Discussion 111. Experimental Data . 1V. Summary . .
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CONTENTS
X
IV-VI AND 11-VI ALLOYS
Chapter 4 Single-Crystal Lead-Tin Chalcogenides Ivars Melngailis and T. C . Harman I. Introduction .
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. . 111. Photovoltaic Detectors . 11. Crystal Preparation
IV. Photoconductive Detectors V. Summary . . .
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Chapter 5 Mercury-Cadmium Telluride and Closely Related Alloys Donald Long and Joseph L. Schmit I. Introduction .
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11. Basic Material Properties
111. IV. V. VI.
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. . . 218 Basic Infrared Detector Theory Applicable to These Materials Crystal Preparation . . . . . . . . . . 233 Detector Fabrication and Properties . . . . . . . . 244 Conclusion . . . . . . . . . . . . 251 253 Appendix. Intrinsic Carrier Concentration versus Temperature in Hg,-.Cd,Te.
THERMAL DETECTORS
Chapter 6 The Pyroelectric Detector E. H . Putley I. The Pyroelectric Effect . . . 11. The Pyroelectric Detector . . 111. Construction ofPyroelectric Detector . Appendix. Electrode Geometry . . . Note Added in Proof
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Chapter 7 Radiation Thermopiles Norman B. Stevens I. 11. 111. IV. V.
Introduction . . . . . . Theoretical Background . . . . . Thermopiles as Radiation Detectors . Properties of Thermopile Radiation Detectors Conclusion . . . . . . List ofSymbols . . . . .
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CONTENTS
HETERODYNE DETECTION AND OTHER SPECIAL TECHNIQUES Chapter 8 Low-Level Coherent and Incoherent Detection in the Infrared R. J . Keyes and T. M . Quist I. Introduction .
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11. Low-LevelIncoherent Detection
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111. Low-Level Coherent Radiation Detection . . . . . Appendix. Thermal Generation-Recombination Noise in Photoconductors
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Chapter 9 Coherent Detection in the Infrared
M . C. Teich I. 11. 111. IV. V. VI . VII.
Introduction . . . . . . . . . . Quantum Theory of Infrared Coherent Detection . . . Measurement of the Signal-to-Noise Ratio . . . . . . . . Detection from a Moving Diffuse Reflector An Infrared Laser Radar . , . . . . . . Photoconductors and Photodiodes in the Infrared: A Comparison Conclusion . . . . . . . . . .
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. 365 . 375 ,389 ,400 . 403 . 406
Chapter 10 Infrared Heterodyne Detection with Gigahertz IF Response F. R. Arams, E. W. Sard, B. J. Peyton, and F. P. Pace I. 11. 111. IV. V. VI. VII.
Introduction . . . . . . . . . . . . Design Formulas for Photoconductive Mixers . . . . . . . . . . . Mixer Response Measurements Using Ge:Cu . IF Preamplifier . . . . . . . . . . . . . Prediction of Performance from Mixer I-V Characteristic . Results on Heterodyne Detection in Ge:Cu . . . . . . Effects of Bias Voltage and Operating Temperature on Mixer Response. . Appendix A. Derivation of Design Equations . . . . . . Appendix B. Effective IF Noise Temperature under Mismatched Conditions . Appendix C. Analysis of Mixer Performance from Mixer I-V Characteristics.
409 410 415
419 420 421 426 429 431 432
Chapter 1 1 Microwave-BiasedPhotoconductive Detector H . S. Sommers. Jr. I. 11. 111. IV.
Introduction . . . . Limitations of Ohmic Contacts Response of Detector-Theoretical Design Details . . .
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xii
CONTENTS
V. VI. VII. VIII.
Performance Factors for Broadband Detectors . . Response of Various IR Photoconductors-Experimental Comparison of Sensitivity with Representative Broadband Areas for Further Research . . . . .
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Detectors
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Chapter 12 Imaging and Display Robert Sehr and Rainer Zuleeg .
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11. Beam-Scanned Imaging Devices
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I. Introduction
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111. Electronically Scanned Photodetector Arrays IV. Image Readout Methods for Photodetector Arrays V. Imaging Characteristics of Photodetector Arrays V1. Array and Scanning Circuit Integration . . VII. Display Devices . . . . . . VIII. Parallel Readout Image Converters . . . AUTHORINDEX. SUBJECTINDEX .
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461 470 483 497 . 505 . 508 . 508 . 520
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Semiconductors and Semimetals Volume 1 Physics of 111-V Compounds C . Hilsum, Some Key Features of 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k . p Method V. L. Bonch-Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of Ill-V Compounds Laura M . Roth and Petros N . Argyres, Magnetic Quantum Effects S. M . Puri and T . H. Geballe, Thermomagnetic Effects in the Quantum Region W. M . Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H . Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H . Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals
Volume 2 Physics of 111-V Compounds M . G. Holland, Thermal Conductivity S. I . Nooikoua, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J . R . Drubble, Elastic Properties A . U. Mac Rae and G. W . Gobeli, Low Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in 111-V Compounds E. Antdncik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in lnSb G. W . Gobeli and F. G. Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in Ill-V Compounds M . Gershenzon, Radiative Recombination in the Ill-V Compounds Frank Stern, Stimulated Emission in Semiconductors
Volume 3 Optical Properties of III-V Compounds Marvin Hass, Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D. L. Stierwalt and R. F. Potter, Emittance Studies H . R . Philipp and H . Ehrenreich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J . Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J . G. Maurozdes, Interband Magnetooptical Erects
xiv
CONTENTS OF PREVIOUS VOLUMES
H . Y. Fan, Effects of Free Carriers on the Optical Properties Edward D . Palik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H . Bube, Photoelectronic Analysis B. 0. Seraphin and H . E . Bennett, Optical Constants
Volume 4 Physics of 111-V Compounds N . A . Goryunova. A . S. Borshchevskii, and D . N . Tretiakou, Hardness N . N . Sirofa,Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV Don L . Kendall, Diffusion A . G . Chynowerh, Charge Multiplication Phenomena Robert W .Keyes, The EfFects of Hydrostatic Pressure on the Propertiesof IIILV Semiconductors L . W . Aukerman, Radiation Effects N . A . Goryunova, F. P . Kesamanly, and D . N . Nasledov, Phenomena in Solid Solutions R. T. Bute, Electrical Properties of Nonuniform Crystals
Introduction
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CHAPTER 1
Characterization of Infrared Detectors Henry Levinstein
I . INTRODUCTION.. 11.
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CHARACTERIZATION OF
. . . . . . . . . . . . . . DETECTORS . . . . . . . . . . .
3 3
I. Introduction Infrared detectors may be characterized by three basic parameters : the spectral range over which they respond, speed with which they respond, and the smallest radiant power they can detect. Some of these parameters arc not absolute quantities, but may depend on the conditions of measurement and on the environment in which the detectors are used. Thus the minimum detectable power, frequently referred to as noise equivalent power (NEP), may vary with the energy distribution of the source; it will also depend on the amount of extraneous radiation which reaches the detector from the thermal background. The parameters may be an inherent property of the detector material, or they may depend on fabrication techniques and on the geometrical design. It is important in the characterization of detectors that measurement techniques are clearly specified, so that they may be reproduced at will. In addition, the physical processes responsible for detector action should be sufficiently well understood that their behavior under conditions other than those prevailing during parameter measurement may be anticipated. 11. Characterization of Detectors
A determination of the parameters may require the measurement of several detector properties, or a single measurement by several techniques. In particular, evaluation of noise equivalent power requires measurement of two quantities: the signal produced by the detector when it is exposed to modulated radiation from a blackbody source, and the detector noise when it is shielded from the blackbody radiation. Among the conditions of measurement which must be specified are the temperature of the radiation
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4
HENRY LEVINSTEIN
source, the modulating frequency, and the amplifier bandwidth. Standardization of blackbody temperature is required because the spectral distribution of the emitted radiation will determine the amount of radiation the detector “sees.” A blackbody at 500°K is usually employed as a radiation source for detectors with response beyond 2p. Since both detector signal and noise may be frequency-dependent, the modulating frequency must be specified. The amplifier bandwidth must be known because it determines the magnitude of the measured noise. In order to minimize the noise variations within the frequency interval over which noise is measured, the amplifier bandwidth must be made as narrow as practicable (usually 4 or 5 Hz, the bandwidth of commercially available harmonic analyzers). The noise equivalent power (NEP) expressing a particular set of measurement conditions may be written as follows : P A NEP(500°K, 900 Hz,5 Hz) = D. (1) SIN
The quantities in parentheses refer to the blackbody temperature, modulating frequency, and amplifier bandwidth, respectively ; S and N represent signal and noise under the conditions of measurement, A the detector area, and PD the radiant power density which reaches the detector from the blackbody. As a matter of convenience the reciprocal of NEP, the detectivity D (in reciprocal watts), is often specified. In order to make possible comparison among detectors, detectivity is often normalized to an amplifier bandwidth of 1 Hz and a detector area of 1 cm’. This yields the parameter D* such that’
The normalization is based on evidence that noise varies as the square root of amplifier bandwidth and that D varies inversely as the square root of detector area. The first assumption is usually well justified, since detectors are generally measured at a frequency where noise is frequency-invariant, or at a sufficiently narrow bandwidth that the frequency variation of noise is insignificant. The second assumption is sometimes not entirely justified and may lead to considerable error in the normalization process. Yet its convenience usually justifies its use, especially where its shortcomings are understood. Infrared detectors are used in a spectral range where they “see,” in addition to the radiation from a given source, considerable radiation from thermal background. The amount and type of background to which the detector is exposed must be specified, since it may affect detector characteristics rather drastically. Unless otherwise specified D* is given for a field R. C. Jones, Proc. I.R.E. 47, 1495 (1959).
1 . CHARACTERIZATION
OF INFRARED DETECTORS
5
of view of 2n sr and a background temperature of 300°K. It is usually possible to calculate what effect different background conditions will have on D*.2 On the other hand, effects on other characteristics, such as the speed of response, may not always be estimated. While D* provides a useful means of comparison among detectors, it is of little value to the system designer who must construct amplifiers to be used in conjunction with detectors. Since the design of the amplifier depends on the magnitude of the signal, usually specified in terms of responsivity (signal voltage per watt incident power) and the nature of the detector noise, information on both quantities must be available. Both noise and responsivity are frequency-dependent. Several types of noise are observed in detectors. Johnson noise3 is the limiting noise in all conductors. It is frequency-invariant in the audio- and radio-frequency regions and is independent of the magnitude of current passing through the detector. It is given by the expression
vj
=
(4KTRAf)”2,
where R is the resistance ofthe conductor in ohms, K the Boltzmann constant (1.38 x l o p z 3J/deg), T the temperature of the detector in OK, and A,f the amplifier bandwidth in hertz. A type of noise known as llfnoise is present in all detectors containing semiconductor elements. This type of noise has a spectrum whose noise voltage varies as llf”. where n is approximately i,but may deviate somewhat from that value.4 Noise due to fluctuations in the generation and recombination of charge carrier^,^ just as llf noise, varies linearly with current. It may be due to the random arrival of photons from the background (photon noise) or to fluctuation in the density of charge carriers as produced by lattice vibration (g-r noise). Its frequency spectrum is determined by the free-charge carrier lifetime. Temperature noise is produced by fluctuations in the temperature of the surroundings, especially the surface on which the detector element is mounted. Information on the speed of response of a detector may be obtained from two types of measurements: the observation of the signal rise and decay times as the detector is exposed to square pulses of radiation having sufficient duration for equilibrium to be established in the detector element, and the determination of the frequency response of the detector as the modulation
* P. Bratt, W. Engler. H. Levinstein, A. U. MacRae. and J. Pehek, lnfrared
Phys. 1. 27 (1961). P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, “Elements of Infrared Technology.” Wiley, New York, 1962. A. U. MacRae and H . Levinstein, Phys. Rev. 119. 62 (1960). K. M. Van Vliet, Proc. I.R.E. 46, 1004 (1958).
6
HENRY LEVINSTEIN
frequency of the incident power is varied. If the signal rise and decay characteristics have an exponential behavior, as expressed by a single time constant, both methods give the same value of time constant. Frequently, detector response to a square radiation pulse consists of a rapid rise, designated by a short time constant, followed by a more slowly increasing signal. Under these conditions the detector speed may be given by the fraction which each behavior contributes to the total signal. For this type of behavior and the even more complicated rise and decay characteristics often observed, a detailed description of measurement techniques accompanied by oscilloscope traces and frequency response curves is usually required. A mere statement of the detector response time may then represent only an order of magnitude estimate. In addition, rise and decay characteristics will depend on the amount of radiation reaching the detector, both from the signal source and from the background. Occasionally, they may vary with the spectral distribution of the signal source. It is thus quite clear that specifications of the speed of response of a detector are only really meaningful if the conditions of measurement are clearly specified and if the data can be extrapolated to the conditions under which the detector is actually being used. The spectral response of a detector may be given in either relative or absolute units. If one is merely interested in the shape of the response, i.e., a comparison of the response of the detector a t several wavelengths, it is sufficient to vary the wavelength of radiation incident on the detector by means of a monochromator and to compare the detector response with one of known response. Absolute response determination requires that the comparison detector be calibrated or that calibration of the unknown be performed with the aid of a standard blackbody source. When this has been accomplished Da*, the detectivity at a particular wavelength, may be specified. The value of D,* at spectral peak, where one exists, is usually more meaningful than D* referred to a blackbody, since it does not require specification of blackbody temperature and gives some indication of the general shape of the spectral response. Of course, Da* and D* are identical for wavelength-invariant response and have a calculable relation when the shape of the spectrum is known. The case where the response rises linearly with wavelength and then drops abruptly represents a large group of detectors. Figure 1 shows the ratio of D* at spectral peak to D* for a 500°K blackbody as a function of long-wavelength threshold (or wavelength for detector peak response).6 In order to present more specific information about detectors, the mechanism responsible for the detector action must be considered.
‘ H. Levinstein, in “Applied Optics and Optical Engineering” Chap 9. Academic Press, New York, 1965.
(R. Kingslake, ed.), Vol. 2,
1, CHARACTERIZATION OF INFRARED DETECTORS
7
A (microns)
FIG.1. Ratio of detectivity at spectral peak to the value for a 500°K blackbody as a function of detector threshold wavelength. The curve assumes ideal photon detectors, where the response for constant energy rises linearly with wavelength and then drops abruptly to zero.
Infrared detectors had their beginning with the blackened thermometer used by Hershel when he discovered infrared in 1800. All infrared detectors for the next century were, like the thermometer, of the thermal type. Radiation incident on an absorbing layer warms the layer. This in turn warms the temperature-sensitive material in contact with the absorber. Incident radiant power is then measured by the changes in the characteristics of the temperature-sensitive material. Many types of thermal detectors have been developed and a large variety of them are commercially available. If it were possible to produce materials with wavelength-invariant absorption, these devices would respond uniformly to equal amounts of incident power over all regions of the electromagnetic spectrum. In practice, no uniform “black” exists, and thus the spectral response of thermal detectors is usually not wavelength-invariant. Since these detectors frequently serve as standards for other detectors with a more rapidly varying spectral response, great care is required in their calibration, especially over a wide spectral range. Because of their slowly varying response with wavelength, blackbody detectivity measurements do not require precise specification of blackbody temperature as long as the incident power is known. Since the response time is determined by the rate at which the element warms and cools, its size, specificheat, and the degree of isolation from the environment determine response time. These factors also influence the minimum detectable power
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HENRY LEVINSTEIN
in such a way that the devices which respond more rapidly usually have lower detectivity. Among the physical phenomena which have been applied in the construction of thermal detectors are the generation of thermal voltages (thermocouples and thermopiles), temperature variation of the resistance of metals and semiconductors (metal and thermistor bolometers), pyroelectric effects, and the variation of gas pressure with temperature (Golay cell). While originally most thermal detectors were operated at ambient temperatures, the development of a variety of semiconductors whose electrical properties change more rapidly in the vicinity of liquid helium temperatures, providing at the same time lower thermal capacities, has led to the development of cooled thermal detectors, most of them of the bolometer type. Conventional thermal detectors operated at ambient temperature have values of D*, when this is applicable, in the range from lo8 to lo9 cm H Z ’ ’ W-’ ~ and a time constant in the millisecond range. Semiconductor bolometers designed for liquid helium temperatures may have detectivities several orders of magnitude larger and time constants in the microsecond range. In contrast to thermal detectors are photon detectors, where the incident photons interact with the electronic energy states. In most conventional photon detectors this interaction results in the liberation of charge carriers and increased conductivity or a photovoltage. Photoconductivity was first observed in selenium in the late 18003, but construction of infrared photon detectors did not progress rapidly until the 1940’s. In contrast to thermal detectors, these devices have a well-defined spectral cutoff, depending on the energy required to free charge carriers in a particular material. The shape of the ideal spectral response, assuming constant quantum efficiency rather than being wavelength-invariant for constant incident energy as in the case of thermal detectors, is wavelength-invariant for constant photon flux up to the threshold wavelength. For constant energy, of course, the ideal response increases linearly with wavelength up to the threshold. Real detectors do not have such idealized response curves. The spectral peak will usually occur near, but not at, the threshold wavelength. The decrease in response after the spectral peak may not be abrupt, and the linear rise with wavelength may show considerable deviation. The relationship shown in Fig. 1 should thus be considered merely as a guide. The response time, rather than being determined largely by geometrical considerations as in the case of thermal detectors, is dependent on free charge carrier lifetimes, a characteristic of the material. Because of the various types of recombination mechanisms, rise and decay characteristics may be rather complex and require careful analysis. The emphasis in the development of photon detectors has been toward response to ever longer wavelengths and shorter time constants. At the same time there has been
1. CHARACTERIZATION OF INFRARED DETECTORS
9
a concerted effort to achieve increased detectivity up to the theoretical limit. The earliest photon detectors consisted of evaporated or chemically deposited layers which required trial-and-error sensitizing techniques. Unfortunately, physical processes responsible for the success or failure of these techniques are still not well understood, even though many of these detectors have been prepared for more than 20 years. The first of the infrared film detectors was TI,&, with a response to 1 . 2 ~ .It finds little application today. It was followed rapidly by the use of PbS, responding to about 3 p ; PbTe, to 6 ,u ; and PbSe, to about 7 p. Advances in semiconductor technology, especially the purification and crystal growing techniques employed for Ge and Si, have led to an entirely new group of infrared photon detectors. Not only was it possible to produce detectors of Ge and Si in the near infrared, but also Ge detectors whose response could be extended to beyond loop by the addition of selected impurities with a variety of activation energies. These extrinsic detectors have two superimposed spectral curves, one due to the host crystal, and the other due to the particular impurity added to germanium. When
L
1010,
3
5
WAVELENGTH
610
30
50
( rn icro ns)
FIG.2. Dependence of DA* at spectral peak on long wavelength threshold for several background temperatures. Calculations assume ideal photoconductive detectors having a 2s-sr field of view.
10
HENRY LEVINSTEIN
semiconductor technology was applied to the synthesis of new compounds, such as InSb or InAs, single-crystal detectors for the intermediate IR region (4-6 p) could be constructed with highly-reproducible characteristics and well-understood behavior. In most recent developments the alloying of compounds, such as HgTe and CdTe or PbTe and SnTe, one with a small energy gap and the other with a larger gap, has made possible the construction of detectors whose long wavelength threshold is dependent on the fractional composition of the compounds and has thereby resulted in detectors with a tailor-made spectral response. While extrinsic single crystal detectors are always used in the photoconducting mode, intrinsic single crystal detectors
lo9
190°K
I
I
-
2
I
3
I
4
I
5
\I 6
7
FIG. 3. Spectral response curves of various intrinsic detectors and their temperature of operation (field of view 1 8 O O ) .
1. CHARACTERIZATION
OF INFRARED DETECTORS
11
such as InSb may be constructed to be either photoconductive or photovoltaic. The functioning of photon detectors depends critically on the detector temperature. As the response extends to longer wavelengths, increased cooling is required to reduce competition between carriers liberated by incident signal photons and those generated thermally. Detectors with response in the 1-3p region may be operated at room temperature; those with response beyond 100 p require liquid helium temperature. Between these extremes cooling requirements vary, depending on, in addition to the spectral cutoff, the type of detector-intrinsic detectors generally require less cooling than extrinsic detectors. Since IR detectors respond to signals in a wavelength range where there is an appreciable photon flux from the background and thus a competition in the liberation of charge carriers between signal and background photons, the distribution and amount of background photon flux affects the detectivity and must be specified. If one assumes under ideal conditions unity quantum efficiency and noise due only to fluctuations in the arrival of background photons, one can evaluate the upper limit of detectivity for various amounts
Theoretical limit (60" angular field)
IGe : Cu Cooled
I
2
5
10
20
30
Wavelength (microns)
FIG.4. Spectral response curves of various extrinsic germanium detectors and their operating temperature (field of view -60').
12
HENRY LEVINSTEIN
and distribution of background photonse2 Such an ideal detector (BLIP) represents an upper bound to the detectivity which may be achieved. Figure 2 shows how DA* at spectral peak for ideal detectors depends both on the long wavelength threshold of the detector and the temperature of the background to which it is exposed. These curves are for a 21r-sr field of view. The detectivity increases as l/sin)6 as the angle 6 subtended at the detector by the background is reduced below 180". The background limited condition requires that the detector be cooled to the extent that thermally generated charge carriers are reduced considerably below those generated by the background. Thus as the background radiation is reduced, the detector will have to be cooled to even lower temperatures. Photon detectors with a 2n-sr field of view and a 300°K background have detectivities at spectral peak above 10'0cmHz''2 W-' and time constants in the microsecond and nanosecond ranges. Figures 3 and 4 show the spectral response curves of some commercially available IR detectors and their cooling requirements.
111-V Compounds
This Page Intentionally Left Blank
CHAPTER 2
Indium Antimonide Photoconductive and Photoelectromagnetic Detectors Paul W.Kruse
I . INTRODUCTION
.
.
.
. .
.
. . . . . .
.
. .
.
15
11. ELECTRICAL PROPERTIES, OPTICAL PROPERTIES. AND LIFETIME VALUES OF IMPORTANCE TO THE
DESIGN OF INSB~ N F R A R E DDETECTORS . .
.
. . . . . . . . . . . . . 2 . Optical Properties . . . . . . . . . . . . . . 3 . Electron and Hole Lifetimes . . . . . . . . . . . 111. THEORETICAL DETECTOR DESIGN . . . . . . . . . . . 4. Photoconductivity . . . . . . . , . . . . . . 5 . Photoelectromagnetic Effect . . . . . . , . . . . I V . PREPARATION OF PHOTOCONDUCTIVE AND PHOTOELECTROMAGNETIC DETECTORS. . . . . . . . . . . . . . . . . 6 . Purification and Crystal Growth . . . . . . . . . . 7. Fabrication ofthe Sensitive Element . . . . . . . . . 8 . Detector Housing Design . . . . . . . . . . . . 1. Electrical Properties .
V , PERFORMANCE OF PHOTOCONDUCTIVE AND PHOTOELECTROMAGNETIC DETECTORS . . . . . . . . . . . . . . . . . 9. Properties of Selected High-Performance Photoconductive and Photoelectromagnetic Detectors . . . . . . . . . . 10. Comparison of Measured Performance with Theory . . . . . 11. Statistical Distribution of the Properties of Large Numbers of 77'K Photoconductive Detectors . . . . . . . . . .
18 18 27 31
39 41 57 62 63 64 67 70 71 74 77
I. Introduction Indium antimonide, InSb, is a direct, small energy gap semiconductor whose semiconducting properties were first revealed by H. Welker in 1952.' Detailed studies of its properties were soon initiated on a worldwide basis, and in the middle and late 1950's it was the subject of numerous scientific investigations. It was soon discovered that InSb had the smallest energy gap of any semiconductor known at that time; its application as a long wavelength infrared detector became obvious, The gap of 0.17 eV at H.Welker, Z . Naturforxh. 7a, 744 (1952); 8a, 248 (1953).
15
16
PAUL W . KRUSE
room temperature indicated it would have a long wavelength limit of approximately 7 p. When cooled with liquid nitrogen the gap increased to 0.23 eV, resulting in a long wavelength limit of 5.5 p. The interest in InSb as an infrared detector stemmed not only from its small energy gap, but also from the fact that it could be prepared in single crystal form by conventional means. Although lead selenide, PbSe, was also a small gap semiconductor, infrared detectors made from it were in the form of thin films prepared by either vacuum evaporation or chemical deposition. The technique of preparing and oxidizing these films was in the nature of an art, rather than a science. Furthermore, the performance of PbSe detectors could not be inferred from a study of the bulk crystal properties. Thus the interest in InSb as an infrared detector material stemmed also from the realization that it was a classical semiconductor whose properties could be analytically determined, leading to the rational design of a high-performance infrared detector. Three modes of operation have been of interest : photoconductivity, the photovoltaic effect, and the photoelectromagnetic effect. Interest in the photoelectromagnetic (PEM) effect was novel ; no infrared detectors had previously been made which operated by this effect. It can be shown that for materials having a high electron mobility and a low direct lifetime the PEM effect is capable of giving rise to a photosignal larger than that from photoconductivity for reasonable values of magnetic field and electric field. Thus early interest existed in the study of the PEM effect in InSb and the fabrication of PEM detectors. The first practical InSb detectors were grown junction photovoltaic ones.’ Techniques of purifying semiconductors require years before purities in the range of 10’4cm-3 or less required for high performance photoconductors are developed. On the other hand, photovoltaic detectors require p-n junctions having majority carrier concentrations on either side of the junction in the lO”-lO’* cm-3 range, Thus in the early stages of development of a new semiconductor, high performance photovoltaic detectors are usually prepared before photoconductive detectors of comparable performance. The first high performance InSb detectors employed grown junctions, followed soon after by the development of a diffused junction detector. S. W . Kurnick e t a ! . , Electrochem. Soc. Spring Meeting (May 1955); G. R . Mitchell, A. E. Goldberg, and S. W. Kurnick, Phys. Rev. 97, 239 (1955); D. G. Avery, D. W. Goodwin, and A. E. Rennie, J. Sci. Instr. 34, 394 (1957). Unpublished work on diffused junction detectors at Texas Instruments, Inc., Dallas; S. J. Nicolosi, L. H . DeVaux. and A. J . Straws. EIectronics(Eng1ish ed.)31,48 (1958); M. E. Lasser, P. Cholet, and E. C. Wurst, Jr., J . Opt. SOC.Am. 48,468 (1958).
2.
INDIUM ANTIMONIDE DETECTORS
17
InSb photovoltaic detectors are to be the subject of another chapter in a forthcoming volume of this series. In this chapter only the photoconductive and PEM modes of operation will be studied. Photoconductive detectors4 have been designed for optimum performance at room temperature (300"K), dry ice temperature (195"K), and liquid nitrogen temperature (77°K). PEM detector^,^ designed to operate only at room temperature, require use of a small permanent magnet having pole pieces which direct the magnetic induction through the sample. To obtain a sufficiently high field, the sample must be narrow, approximately 1 mm or less, and the pole pieces must nearly touch the sample edges. If the detector is to be cooled, one of two geometries must apply: The entire magnet can be placed within the vacuum space, necessitating a clumsy Dewar design with a large heat capacity, or an extremely narrow Dewar can be used which is capable of fitting between the pole pieces of an uncooled magnet. In the latter, the problem is one of constructing a double-walled Dewar with an extremely small clearance between the walls. Neither approach is satisfactory. Thus this chapter deals with InSb photoconductive detectors operating at room temperature, dry ice temperature, and liquid nitrogen temperature, and with PEM detectors operating at room temperature. To lay the basis for a prediction of detector performance, the following part discusses those electrical properties, optical properties, and excess-carrier lifetime values of InSb which are of importance to detector design. This is followed by a part concerned with theories of the photoconductive and PEM effects in InSb, in which expressions are derived for the spectral responsivity and detectivity for each detecting mode and operating temperature. Part IV deals with the practical aspects of detector preparation, including growth of high-purity InSb crystals, sensitive element fabrication by such methods as photolithography, and design details of detector housings. Finally, Part V considers the measured performance of representative detectors of each type, compares performance with theory, and ends with information on the statistical distribution of the values of the performance parameters of two large groups of 77°K photoconductive detectors. Among the earliest papers are: D. G. Avery, D. W. Goodwin, W. D. Lawson, and T. S. Moss, Proc. Phys. SOC.(London)B67,761(1954);D. W .Goodwin, J . Sci. Instr. 34,367 (1957);Awry et al.'; Nicolosi et al.3;L. H. DeVaux and A . J. Strauss, Electrochem. SOC.FuNMeeting (October 1957); H. P. R. Frederikse and R. F. Blunt, in "Photoconductivity Conference" (R.G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 414. Wiley, New York, 1956; S. W. Kurnick and R. N. Zitter, J. Appl. Phys. 27, 278 (1956). Early papers include: Nicolosi et aL3; Kurnick and Zitter4; C. Hilsum and I. M. Ross, Nature 179, 146 (1957); C. Hilsum, Instr. Prac. 12, 857 (1958);P. W. Kruse, J. Appl. Phys. 30. 770 (1959);P. W. Kruse, Electronics33,62 (1960).H. P. R. Frederikse and R.F. Blunt, Proc. I.R.E. 43, 1828 (1955) summarize studies of all three modes of operation in InSb prior to 1955.
18
PAUL W . KRUSE
11. Electrical Properties, Optical Properties, and Lifetime Values of Importance to the Design of InSb Infrared Detectors Proper design of an infrared detector which will operate in a specified mode at a given temperature requires a detailed knowledge of the properties of the semiconductor from which it is made. The equations to be found in Part I11 relate figures of merit such as the responsivity and detectivity to the internal parameters of the semiconductor, including electron and hole concentrations, mobilities, and lifetimes. In general, these internal parameters are dependent upon the purity of the semiconductor. Therefore it is not sufficient to tabulate, say, the electron mobility at 77°K. Instead, the dependence of mobility upon purity must be displayed graphically. The material in this section has been selected from the many publications and review articles in the literature of InSb.6-’ Of particular value has been the work of Hilsum and Rose-Innes,* who succinctly summarize much information on the electrical properties of InSb containing shallow donors and acceptors. 1. ELECTRICAL PROPERTIES
a. Dependence of the Forbidden Energy Gap and Intrinsic Carrier Concentration upon Temperature Indium antimonide is a direct gap semiconductor whose conduction band minimum and valence band maximum are located at k = 0. Because of the small energy gap, the conduction band follows the nonparabolic behavior postulated by Kane.I4 The forbidden energy gap exhibits the conventional negative temperature coefficient as illustrated in Fig. 1, which is from the “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 1, Physics of
111-V Compounds, 1966; Vol. 2, Physics of 111-V Compounds, 1966; Vol. 3, Optical Properties of 111-V Compounds, 1967. Academic Press, New York. K. F. Hulme, in “Materials Used in Semiconductor Devices” (C. A. Hogarth, ed.), p. 115.
’
Wiley (Interscience), New York, 1965. C. Hilsum and A. C. Rose-Innes, “Semiconducting 111-V Compounds.” Macmillan (Pergamon), New York, 1961. 0. Madelung (translated by D. Meyerhofer), “Physics of 111-V Compounds.” Wiley, New York, 1964. l o H. Welker and H. Weiss, Sdid State Phys. 3, 1 (1956). F. A. CunneH and E. W. Saker, Prog. Semicond. 2, 35 (1957). T.S. Moss, Prag. Semicond. 5, 191 (1961). l 3 T. S. Moss, “Optical Properties of Semiconductors.” Academic Press, New York, 1959. l4 E. 0. Kane, J . Phys. Chem. Solids 1, 249 (1957).
’’ ’’
2.
19
INDIUM ANTIMONIDE DETECTORS
o‘ -320
I
\
O
> (3
U 2
0.20
I w
t
I
F,C
th P
data (circles) of Roberts and Q~arrington.’~ The data (squares) compiled by Long16 represent values believed to be most accurate at 0, 77, and 300°K.
data of Roberts and Quarringt~n,’~ with additional points from Long’s review paper. The intrinsic carrier concentration as a function of temperature” is illustrated in Fig. 2. The room temperature value is 1.6 x 10’6cm-3. Because of the steep dependence of the intrinsic concentration upon temperature at low temperatures, the exact value at 77°K has not been established. It is most probably in the 10” cm-j range. V. Roberts and J. E. Quarrington, J . Electron. 1, 152 (1955). The curve is that listed as E&, representing the value of photon energy at which the measured absorption coefficient equals 100cm l 6 D. Long, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 1, Physics of 111-V Compounds, p. 143. Academic Press, New York, 1966. ” C . Hilsum and A. C. Rose-Innes,’ p. 122. The data have been compiled from D. J. Howarth, R. H. Jones, and E. H. Putley, Proc. Phys. Soc. (London)70, 124 (1957); and from C. Hilsum and R. Barrie, Proc. Phys. Soc. (London) 71, 676 (1958). l5
’.
20
PAUL W . KRUSE
b . Dependence of the Hall Coefficient, Electrical Conductivity, and Carrier Mobilities of InSb Containing Shallow Donors and Acceptors upon Temperature and Carrier Concentration
Most of the electrically active impurity atoms in InSb, whether donors or acceptors, have shallow activation energies (see Table I, after Hulme'). At 77°K or above-the temperature range of interest for photoconductive and photoelectromagnetic InSb detectors-these impurity centers are thermally ionized. Data pertinent to InSb containing these shallow centers are discussed in this section. Because one approach to preparing InSb detectors operating in the photoconductive mode at 77°K is to compensate residual donors with Ge-a deep lying acceptor-the following section will briefly discuss the electrical properties of InSb containing Ge. lo'*
(0''
?-
I 2
16
10
.-
c
IS
I0
I 0l4
200
300
400
so0
T (DEG K )
FIG.2. Oependence of the intrinsic concentration ni of InSb upon temperature. (After Hilsum and Rose-Innes.'')
2.
INDIUM ANTIMONIDE DETECTORS
21
TABLE I ENERGIESIN INSB"
IMPURITY IONIZATION
Element
Na, (Li?)
cu
Electrical effect
Donor Double acceptor
Separation of level from conduction (valence) band edge for donor (acceptor) (ev)
Lower level : 0.023 (Hall effect) 0.026 (photoconductivity) Upper level : 0.056 (photoconductivity)
Double acceptor
Lower level : 0.023 (Hall effect) 0.028 (photoconductivity) Upper level : 0.039 (photoconductivity)
Au
Double acceptor
Lower level: 0.032 (Hall effect) 0.043 (photoconductivity) Upper level : 0.066 (photoconductivity)
Mg, Zn. Cd, Hg
Acceptor
A1 Ga
Acceptor Neutral
Si
Acceptor
Ge
Acceptor
Sn
Donor
Pb
Donor or neutral?
S, Se, Te
Donor
Mn
Acceptor
a
0.0075 Zn(?) (Hall effect)
0.10
Usually merged with conduction band at low magnetic fields
After compilation by Hulme.'
Figures 3 and 4 (from Hilsum and Rose-Innes*) illustrate typical Hall coefficient and conductivity data on reasonably pure n- and p-type InSb samples over the temperature interval between room temperature and 77°K. The temperature independent portions of the Hall curves indicate that the samples are thermally ionized in that interval. Figure 5 illustrates the temperature dependences of the electron and hole mobilities of samples of
22 PAUL W . KRUSE
FIG.3. Dependence of the Hall coefficient R , upon temperature for n-type and p-type samples of InSb. (After Hilsum and RoseInnes. *)
FIG.4. Dependence of the electrical conductivity c upon temperature for the n-type and p-type samples of Fig. 3. (After Hilsum and Rose-Innes.')
2. I.
23
INDIUM ANTIMONIDE DETECTORS
n = 2 x 10'4CM-3
loGI 2. n = 101SCM-3
3.n = i0'6CM-3
1.0
4. p
.
3x 10'4CM-3
5. p = 4x 1015CM-3 6. p = 3x 10'bCM-3
10
I00
I 000
T (OEG K )
FIG. 5. Dependence of the electron and hole mobilities upon temperature for n-type and p-type samples of InSb. (After Hilsum and Rose-Innes.8)
n- TYPE SAMPLES \
\
8-
\ \
\rn-
TYPE
\
\
6-
-
I
I0''
H6
@
F6
813 S2 p-TYPE SAMPLES
Q
%'"b,
p TY >:p
0-
PI
@
0
B
'\
2-
GI
0
8 c4
fi
4-
8
I
6
ZI
- -*Wsp , --s-@--+T-+ I
I0l5 1o16 1018 1 0 ~ ~ IMPURITY CONCENTRATION (CM-'1 FIG.6. Dependence of the electron mobility pn at 77°K upon purity in n-type and p-type InSb. (After Hilsum and Rose-Innes.*)
24
PAUL W . KRUSE
l0,OOO
-
c4 FI 8 F7 0 H3 A H6 8 PI s2 x
+
8.000-
C)
W
v)
6,000-
Nz
I
0
0
-$
a\
@\
zI
4,000-
2,000-
0
\ I
I
--------. ..
~
FIG.7. Dependence of the hole mobility / I , , at 77°K upon purity in p-type InSb. (After Hilsum and Rose-Innes.8)
varying purity.8 The maximum mobility of both carriers occurs in the 50-100"Krange. Figures 6 and 7 illustrate the dependence of the electron and hole mobilities, respectively, upon impurity concentration at 77°K.' Similar data for the electron and hole mobilities at room temperature8 are illustrated in Figs. 8 and 9. If the electron and hole mobilities were equal at a given temperature, the maximum resistivity would occur for intrinsic material. Because the electron 8 x lo4
-Y
6x104
u)
> 'N
-3
THEORY FOR p-TYPE /"", SAMPLES
+
\'\ 'b,
@, '
',a
\
4x104
Li 2 x 1 0 ~ C
d4
dS
i0l6
ide
10"
IMPURITY CONCENTRATION (CM-')
FIG.8. Dependence of the electron mobility pE at room temperature upon purity in n-type and p-type InSb. (After Hilsum and Rose-Innes.')
2.
2s
INDIUM ANTIMONIDE DETECTORS
cI
600
-
V W
m
>
I
\
\
a x
K1
s2
4
0
10'~
l0l5
lo1'
l0l6
l0l8
IMPURITY CONCENTRATION ( C M 3 )
FIG.9. Dependence of the hole mobility p, at room temperature upon purity in p-type InSb. (After Hilsum and Rose-Innes.')
0*051
n
0.04
1.0
0.75
0.5
0.2 5
0
(y)
FIG. 10. Dependence of electrical resistivity p o upon acceptor concentration N , at room temperature in InSb; n,/p is the intrinsic concentration to free hole ratio. (After Hilsum.")
mobility in InSb at room temperature is roughly two orders of magnitude greater than the hole mobility, maximum resistivity is found in p-type material. Figure 10 (from Hilsum") illustrates the dependence of the roomtemperature resistivity upon acceptor concentration.
'* C . Hilsum, Solid
State Phys. Electron. Telecornmun., Proc. Intern. Conf: Brussels, 1958 2 (1960); "Semiconductors, Part 2" (M. DCsirant and J. L. Michiels, eds.), p. 733. Academic Press, New York, 1960.
26
PAUL W . KRUSE
The large electron mobility and mobility ratio give rise to pronounced transverse magnetoresistance effects at low magnetic fields in InSb at room temperature. Room temperature magnetoresistance data18 are illustrated in Fig. 11.
0
5000
10,000
MAGNETIC FIELD (GAUSS)
FIG. 11. Dependence of the magnetoresistivity ratio A p / p o upon magnetic field and hole concentration p o at room temperature. (After Hilsum.")
c. Dependence of the Hall Coeficient and Mobility of Ge-Doped InSb upon Temperature Cunningham et ~ 1 . 'have ~ shown that Ge in InSb introduces a shallow donor level and a shallow acceptor level, both of which are thermally ionized at 77°K and above, and a deep acceptor level whose ionization energy with respect to the valence band is about 0.1 eV. By introducing Ge into n-type InSb shallow donors can be compensated, resulting in InSb having resistivities at 77°K in the 1-100 ohm-cm range. The temperature dependences of the Hall coefficient and electron and hole mobilities for InSb containing Ge are illustrated in Figs. 12 and 13, respectively. l9
R. W. Cunningham, E. E. Harp, and W. M. Bullis, Proc. Intern. Con$ Phys. Semicond., Exeter, 1962, p. 732. Inst. ofPhys. and Phys. Soc., London, 1962.
2.
21
INDIUM ANTIMONIDE DETECTORS
Io6
-
lo5
-1
3
0
u
\
n
5
-u 1
P -
4
10
SAMPLE
lo3
lo2
4
6
N A - N ~ ( C ~ - N,,(c~-~) ~)
0
187T
2 . 5 0 ~l0l2
1.30~loi4
A
187M
2.80
o
1878
6 . 2 5IOl3 ~ 2 . 3 6 ~IOl4
8
10
12
loi4
6.65~10'~
14
16
1 0 ~(DEG 1 ~K-'1
FIG.12. Dependence of the Hall coefficient R , upon temperature for Ge-doped InSb having the stated excess acceptor concentrations (NA-ND).The solid curves were computed assuming a deep acceptor ionization energy of 0.106eV and the deep acceptor concentrations N,, shown. (After Cunningham et a1.")
2. OPTICALPROPERTIES a. Dependence of the Optical Absorption Coeficient upon Energy, Temperature, and Purity The dependence of the optical absorption coefficient of InSb upon photon energy at 298"K, 90"K, and 5°K is illustrated in Fig. 14 (after
28
PAUL W . KRUSE
TIDEG K l
FIG.13. Dependence of the electron and hole mobilities upon temperature for the Ge-doped InSb samiles shown in Fig. 12. The electron mobilities indicated by the ordinate scale are 0.1 times the actual value. The mobility ratios of samples 187T, (bT),and 187B, (b,) are included. (After Cunningham et a!.”)
Gobeli and Fan2’). Details of the temperature dependence of the lowenergy portion of the absorption edge are displayed in Fig. 15 (from Roberts and Quarrington”). Because of the very small effective mass ratio of free electrons (0.0155 at liquid helium temperature’ 6), the conduction band density of states is small. Since the effective mass ratio of free holesI6 is approximately 0.4, the Fermi level lies in the conduction band at room temperature for InSb whose free electron concentration is greater than about 5 x lo1 cm- Intrinsic absorption of a photon requires an energy sufficient to cause excitation
’.
2o
’
G . W. Gobeli and H. Y. Fan, Semiconductor Research, Second Quarterly Report, Purdue University, 1956. [Quoted by E. J. Johnson, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 3, Optical Properties of 111-V Compounds, p. 153. Academic Press, New York, 1967.1 See Roberts and Quarrington.”
29
2. INDIUM ANTIMONIDE DETECTORS
lo4 3 10
-
2 10
-
-
1
I
5 Y
0
-T
a 5°K
I
10
+
\
I
T
- 90°K I
I
I
I
I
FIG.14. Dependence of the optical absorption coefficient a of pure InSb upon photon energy hv and temperature. (After Gobeli and Fan.”)
from the top of the valence band to the Fermi level in such degenerate material. Thus the optical absorption edge shifts to shorter wavelengths with increasing free electron concentration, as illustrated in Fig. 16 (see Hrostowski et ~ 1 . ~ ~ ) . b. Dependence of the Refractive Index and Extinction Coefficient upon Wavelength Seraphin and Bennettz3 have tabulated values of refractive index and extinction coefficient of InSb over the wavelength interval from 0.049 p
‘’ H. J. Hrostowski, G. H. Wheatley, and W. F. Flood, Jr., Phys. Rev. 95, 1683 (1954). 23
B. 0. Seraphin and H. E. Bennett, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 3, Optical Properties of 111-V Compounds, p. 499. Academic Press, New York, 1967.
30
PAUL W . KRUSE
WAVELENGTH ( p )
Fic. 15. Dependence of the optical absorption coefficient a of InSb upon photon wavelength and temperature. (After Roberts and Quarrington2l)
to 12.06~.Table I1 lists the values compiled by them from the data of Philipp and E h r e n r e i ~ hMoss , ~ ~ et and Kurnick and which apply to the 1-8 p interval. c. Dependence of the Quantum EfiEciency ofthe Internal Photoefect upon Energy
Tauc and Abrahamz7have determined the quantum efficiency for intrinsic photoexcitation at room temperature, i.e., the number of free hole-electron pairs produced per absorbed photon. Their data are illustrated in Fig. 17 for a sample containing 6.4 x c m - j acceptors. The rise in quantum efficiency with increasing energy for energies greater than 0.5 eV is attributed to the generation of additional hole-electron pairs by impact ionization, i.e., the interband Auger effect, Gibson et ~ 1 . ~have ~ ‘ observed photoconductivity at 1 0 . 6 ~using a Qswitched CO, laser. They attribute the effect to a two-photon absorption process. 24
H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
’’ T. S. Moss. S. D. Smith, and T . D. F. Hawkins, Proc. Phys. SOC.(London) 870, 776 (1957). 26
*’
S. W. Kurnick and J. M. Powell, Phys. Rev. 116, 597 (1959). J. Tauc and A. Abraham, Czech. J. Phys. 9.95 (1959). [Quoted by E. AntonEik and J. Tauc, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 2, Physics of 111-V Compounds, p. 245. Academic Press, New York, 1966.1 A. F. Gibson, M. J. Kent, and M. F. Kimmit, Brit. J . Appl. Phys. Ser. 2, I, 149 (1968).
2.
INDIUM ANTIMONIDE DETECTORS
31
TABLE IT WAVELENGTH DEPENDENCE OF REFRACTIVE INDEXn AND EXTINCTION COEFFICIENT k IN INSB‘
1.03 1.24 1.55 1.60 1.80 2.00 2.07 2.50 3.00 3.50 4.00 4.50 5.00 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.50 7.87 8.00 a
n
k
Reference
4.24 4.15 4.08
0.32 0.26 0.20 0.18 0.17 0.17
24 24 24 25 25 25 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 26 26 25 25
4.03 0.15 0.13 0.12 0.11 0.10 0.09 I 0.074 0.072 0.070 0.068 0.066 0.063 0.059 0.055 0.049 0.037 0.025 5.2 x 10-3 4.001 3.995
After Seraphin and Bennett.23
3. ELECTRON AND HOLELIFETIMES A knowledge of the dependence of electron and hole lifetimes upon purity and temperature is important to proper detector design, since the lifetime values can affect not only the photosignal, but also the response time and noise. In general, the determination of the proper model of the recombination mechanisms which limit the lifetimes is a difficult task. Those interested in a detailed review of the recombination processes operable in semiconductors are referred to Blakemore.28 As pointed out in Part 111, following the analysis of Zitte~-,~’ the photoconductive response time zpc and the photoelectromagnetic response time 28
29
J. S. Blakemore, “Semiconductor Statistics.” Pergarnon Press, New York, 1962. R. N. Zitter, Phys. Rev. 112, 852 (1958).
32
PAUL W . KRUSE
tpEM in general have differing dependences upon the electron lifetime t, and the hole lifetime tp.Thus, for example, determination of the frequency response of the photoconductive signal reveals zpc, but not tpEM, z,, or t p .In
2
3
c
0.010'
4
0.0075'
3
4
5
WAVELENGTH
6
7
8
(pl
FIG.16. Dependence of the optical transmission of n-type InSb upon wavelength A'at room temperature. The free electron concentration ranges from 5 x loL5cmU3for curve 1 to about 10'' ~ r n for - ~curves 4 and 5. The sample thicknesses in inches are shown. (After Hrostowski et dzz)
only two special cases are tpc and tpEM equal. The first is when z, equals tp, in which event zpEMand tpc are both equal to t, and tp.The second is when the electron concentration multiplied by the mobility ratio equals the hole concentration, in which event tpEM and tpcare equal to each other but not to z, and tp.
2.
0.5
33
INDIUM ANTIMONIDE DETECTORS
0.4
0.8
0.6 Ef
1.0
[eq
FIG.17. Dependence of the quantum efficiency of the internal photoeffect upon photon energy E , in InSb at room temperature. (After Tauc and Abraham2’)
I
b
t*
TPEM 0
TPC
+ O
I.
I I I I
I
a
I I I
I 11
a
INTRINSIC CONCENTRATION
I I I 1
I I
FIG.18. Dependence of zK and rPEMupon hole concentration po in p-type InSb at 300°K. (After Zitter er a / . 3 2 )
34 PAUL W . KRUSE
FIG. 19. Dependence of T~ upon hole concentration po in p-type lnSb at 200°K. (After Zitter et aL3')
FIG. 20. Dependence of zpCand tpEM upon hole concentration p o in p-type InSb at 77°K. (After Zitter et ~ 1 . ~ ' )
2.
'.
\
35
INDIUM ANTIMONIDE DETECTORS
T = 84°K
-Nt
a
14
-3
0 . 8 x l O cm
'
1
FIG.21. Fermi level dependence of electron and hole lifetimes for n- and p-type samples of InSb at various carrier concentrations at 84°K. Solid curves are carrier lifetimes calculated by using the model of two level centers. The dashed curves show the variations of the carrier concentration p or n and effective impurity concentration ( N A-ND)or (N,- N A ) . (After Lag and Fan.")
Wertheim,30 who studied recombination in n-type and p-type InSb over the temperature interval from 130 to 250"K, pointed out that the recombination mechanism at the lower and middle portions of the temperature interval was of the low level Shockley-Read3' type in which the electron and hole lifetimes were equal. Zitter et aL3' showed that the dominant recombination mechanism in n- or p-type InSb of reasonable purity at room temperature is a direct Auger process. Thus the data of Wertheim and of Zitter et al. showed that the electron and hole lifetimes were equal in InSb at room temperature, down to temperatures of the order of 130°K. Figure 18 illustrates the dependences of s~~~ and zpc upon hole concentration at 300°K. G . K. Wertheim, Phys. Rev. 104,662 (1956). W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952) 32 R. N. Zitter, A. J. S t r a w , and A. E. Attard. Phys. Rev. 115,266 (1959). 30
31
36
PAUL W . KRUSE
c /-
10-
i
t
1 0 ~ (1D E ~ G K-’)
FIG.22. Dependence of spc. rPEM,I,, and tP upon temperature in a sample of p-type InSb having 3 x 10” cm-3 excess acceptors. (After Zitter et ~ 1 . ’ ~ )
Figure 19 shows the dependence of zpc upon free hole concentration at 200°K. In p-type InSb at 77°K the hole and electron lifetimes are far different (see Fig. 20). It can be seen that zpc depends inversely upon the free hole concentration p o , whereas zPEMis much less and is independent of the hole concentration. The data are indicative of unequal minority and majority carrier lifetimes. On the other hand, in n-type InSb of moderate to high purity the lifetimes are equal. Figure 21 (after Laff and Fan33) shows the dependence of z, and zp upon purity at 84“K, assumed to be representative of the 77°K data. The abscissa is the energy of the Fermi level with respect to the valence band edge (left side) and conduction band edge (right side). Thus in p-type InSb at 84°K the hole lifetime t pincreases as p o is reduced (ie., as the Fermi level moves toward the right from the extreme left), but the electron lifetime t, remains constant. In n-type InSb at 84°K the two
’’ R. A. Larand H. Y. Fan, Phys. R w . 121, 53(1961).
2.
37
INDIUM ANTIMONIDE DETECTORS
CONC ENT RAT10N OF ACC E PTOR S
N14 ~ x I O : ~ C M - ~ ' N 5 1.2~10 CM-3 N19 10'4CM'3
N 4 4 2x10"CM-3 N 2 2 8 x 1012CM-3* N 2 3 4 X 1013CM-3 N I O 2 n 10'4CM-3
lrsJ -
HOLE CONCENTRATION AT 7 7 ' K . SINCE ACCEPTORS WERE NOT COMPLETELY IONIZED AT 77.K
2 -
1 2-
z X 1tg1
I 6
I
5
4
I
I
1
1
1
7
8
9
10
II
103/TCOEG K - ' )
FIG. 23. Dependence of zK upon temperature and acceptor concentration in p-type InSb. (After Nasledov and Smetannikova.")
v W ro N13
U
N16 CONCENTRATION OF DONORS N4 2 x 1013~m-3
N15
Id8
4
N13
3 . 8 x IOl3&i3
~
N16 8 I
I
5
6
~
N3
~
I . I x 10'4c63
1 . 7 ~d 4 c m 3
~
~
n
i
I
I
1
1
1
7
e
9
10
I1
~
1 0 ~ (1 DEG ~ K-')
FIG.24. Dependence of rpc upon temperature and donor concentration in n-type InSb. (After Nasledov and S m e t a n n i k o ~ a . ~ ~ )
w
lo6 L
a,
I
10' -
-u
IP-
-
w ln
-e
10
V W
cn
u
lo9-
b
lo9
-10
10
-
-LO
10 0
2
4
6
E
1 01 2
14
IO~/T(DEG.K-')
- q l , 10 0
2
4
6
8
10
I
I
I
I2
14
16
1 0 ~(DEG 1 ~K - I )
FIG.25. Dependences of zPc and rpEMupon temperature for Gedoped InSb. Curves 1'-6': ipcfor samples 1 4 . Curves 1-7: rPEM for samples 1-7. Free hole concentrations at 77°K are as follows :Sample 1 : 5.6 x 10l~Cm-3;2: 1.9 x 1014cm-3; 3: 3.4 x 10'4cm-3; 4: 7.1 1 0 ' 4 ~ m - 3 ; 5 : 6.3 x 1 0 ' 5 ~ m - 3 ;6: 1.0 x 1016cm-3; 7 : 1.7 x 1 O I 6 ~ m - (After ~ . Gulyaeva et d3')
FIG.26. Dependences of rpc (curves I) and T~~~ (curves 11) upon temperature for InSb with Ge and Au impurities. Sample 8, Ge-doped, has a free-hole concentration at 77°K of 1.7 x IOl3 Sample 9, Au-doped, has a free-hole concentration at 77°K of4.9 x 10" cm-j. (After Gulyaeva et al.")
2.
INDIUM ANTIMONIDE DETECTORS
39
lifetimes are equal, having a value of 8 x IO-’sec. The recombination mechanism at 77°K (or 84°K) in n-type InSb is the low level Shockley-Read type in which the recombination center concentration is far less than the majority carrier concentration. In p-type InSb, however, the recombination center concentration is greater than the majority carrier concentration, leading to unequal lifetimes. The general temperature dependences of zpc, z ~ z, ~and~ z p in , p-type InSb are shown in Fig. 22. Data on p-type samples of higher purity, and on n-type samples (after Nasledov and Smetannik~va’~)are illustrated in Figs. 23 and 24, respectively. Hollis el aL,35extending the analysis of Laff and Fan,33 believe such data can be interpreted in terms of two sets of single level, donorlike recombination centers. On the other hand, Volkov and G a l a ~ a n o vbelieve ~ ~ that a single level recombination center model applies at these temperatures in p-type InSb. From studies of tpCand zpEMbetween 77°K and 170°K in Ge-doped and Au-doped InSb (see Figs. 25 and 26), Gulyaeva et af.37found that these impurities do not introduce recombination centers. Thus their data tend to confirm the structural defect recombination center mechanism postulated by Laff and Fan.33
111. Theoretical Detector Design The previous part has presented values of parameters pertinent to the performance of InSb infrared detectors. The present part will employ these values to determine the optimum design of detectors operating at 3 W K , 195”K, and 77°K. Equations will be derived illustrating the dependences of spectral detectivity and responsivity upon the purity of the InSb. The design equations for the photoconductive and photoelectromagnetjc effects can be exceedingly complex if all the parameters which play a part in the effects are included. Thus all who employ the equations make one or more simplifying assumptions. For example, Kurnick and Zitter3’ assume the optical absorption coefficient is infinite, the sample is thick, and the electron and hole lifetimes are equal. Kruse et ~ 2 1 also . ~ ~assume the absorption coefficient to be infinite and the lifetimes equal, but take into account D. N. Nasledov and Y u . S . Smetannikova, Fiz. Turrd. Tela 4, 110 (1962) [Souiet Phys-Solid State (English transl.) 4, 78 (1962)l. 35 J. E. L. Hollis, S. C. Choo, and E. L. Heasell, J . Appl. Phys. 38, 1626 (1967). 3 6 A. S. Volkov and V. V. Galavanov, Fiz. Tekh. Poluprou. 1, 163 (1967) [Soviet Phys.-Semicond. (English transl.) 1, 129 (1967)l. 37 A. S. Gulyaeva, V. S. Ivleva, and M. I . Iglitsyn, Fiz. Tuerd. Tela 8, 2472 (1966) [Soviet Phys.Solid State (English transl.) 8, 1972 (1967)l. S. W. Kurnick and R. N. Zitter, J . Appl. Phys. 27, 278 (1956). 39 P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, “Elements of Infrared Technology.” Wiley, New York, 1962. 34
40
PAUL W . KRUSE
sample thickness and unequal front- and back-surface recombination velocities. ZitterZ9assumes infinite absorption and thick samples, but considers the case in which trapping occurs so that the carrier lifetimes are not equal. D e V ~ r e , ~ who ’ considers only photoconductivity, removes the restriction on infinite optical absorption, but assumes both lifetimes are equal. Moss?’ who also considers only photoconductivity, also includes finite values of the optical absorption coefficient, but assumes both lifetimes to be equal and the sample to be thick compared to a diffusion length. Laff and Fan33 remove the restriction on the value of the optical absorption coefficient and allow unequal carrier lifetimes, but restrict the analysis to samples whose thickness is large compared to an ambipolar diffusion length, and assume the front and back surface recombination velocities to be equal. Nearly all authors assume the sample dimensions to be infinite in the plane of the incident, normal radiation, and the quantum efficiency to be unity. Of the authors mentioned above, only Kruse et introduce expressions for noise and solve for the detectivity. The present discussion will not attempt to derive or employ the most rigorous expressions for the photoconductive or PEM signals. Rather, the most simple of the expressions which reasonably describe InSb will be used, namely, those of Zitter.29 His expressions permit unequal values of the hole and electron lifetimes, the case which applies to the most important of the InSb infrared detectors, namely, the p-type photoconductive one operating at 77°K. The purpose of the derivations of the spectral responsivity and detectivity, which begin with Zitter’s expressions, is to determine the manner by which the one material parameter under direct control, namely, the material purity, influences these derived quantities. Thus it will be possible to determine the optimum purity for operation in the photoconductive and PEM modes at 300”K, and the photoconductive mode at 195°K and 77°K. Operation in the PEM mode at these lower temperatures will not be considered because it offers no performance advantage and entails means for cooling the magnet. The derivation of the spectral detectivity, given the proper expression for the spectral responsivity, hinges upon the proper choice of noise expression. Since no electrical bias is employed in the PEM effect, only thermal (Johnson) noise is found. The mechanisms operable in photoconductive detectors are thermal, generation-recombination (g-r), and l/f power-law noise. Of these, llfpower-law noise shall be ignored because it is not presently possible to write an expression for the magnitude of the noise which explicitly depends upon material parameters. In addition, this noise usually disappears in thermal or g-r noise at the higher electrical frequencies. 40 41
H. B. DeVore, Phys. Rev. 102, 86 (1956). T. S. Moss. in “Semiconductors and Scmimetals” (R. K. Willardson and A. C. Beer. eds.), Vol. 2. Physics of 111-V Compounds. p. 205. Academic Press, New York, 1966.
2.
INDIUM ANTIMONIDE DETECTORS
41
As Long42 has pointed out, it is important that the proper form of the several g-r noise expressions be employed. Thus the analyses for operation in the photoconductive mode at 77°K will employ differing expressions for n-type and p-type materials because of their differing recombination mechanisms. Since the mechanism is the same for n- and p-type InSb at 195"K, a single expression will suffice. Finally, the question of the transition from g-r limited performance to background limited (BLIP condition) will not be treated analytically. It is not at all clear that the phonon induced g-r noise and photon induced background noise are statistically independent and therefore can be added in quadrature. This problem becomes particularly acute when the recombination process is other than direct radiative, for example, of the Shock1ey-Read3' type. In his review of noise in solid state photodetectors Van Vliet43 derives expressions for the background limited detectivity and the g-r noise limited detectivity, but not for the transition between the two. The present analysis will do likewise. 4. PHOTOCONDUCTIVITY ZitterZ9has shown thati,,pc, the photoconductive short-circuit current per unit sample width, is given by is,,, = qNPnZPC(1 + l/b)J%, (1) where q is the electronic charge, N is the number of absorbed photons per unit surface area per unit time which produce intrinsic holeeelectron pairs with unit quantum efficiency, p,, is the electron mobility, b is the ratio of electron mobility to hole mobility, E x is the applied electric field strength, and tpC is the photoconductive response time. The principal assumptions upon which Eq. (1)is based include the following. Recombination in the bulk only is allowed; i.e., the front and back surface recombination velocities are assumed to be negligible.43" Optical absorption is assumed to take place entirely at the irradiated surface. Intrinsic excitation of the holeeelectron pairs is assumed to take place with unit quantum efficiency. That the last assumption is reasonable for InSb is illustrated by the quantum efficiency data of Taw2' (see Fig. 17). The photoconductive response time is shown by Zitter29 to be given by
D. Long, Infrared Phys. 7, 169 (1967). K. M. Van Vliet, Appl. Opt. 6, I145 (1967). 43"Rittner436has shown that for intrinsic processes where the radiation is strongly absorbed, photoexcitation may be considered to be uniform throughout the sample if the effective diffusion length is much greater than the sample thickness. 43bE. S. Rittner, in "Photoconductivity Conference" (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 215. Wiley, New York, 1956. 42
43
42
PAUL W . KRUSE
Here t, is the electron lifetime and t pis the hole lifetime. For monochromatic radiation of wavelength A, N is related to the irradiance H , (radiant power per unit area) by
(3)
N = H,A/hclw,
where h is Planck’s constant, c is the speed of light, 1 is the sample length between electrodes, and w is the width. Thus the open circuit voltage uovPc is given by V0,PC
=
is,,cwR
*
where R is the sample resistance. The spectral responsivity
(4)
is therefore
where d is the sample thickness, and po, the electrical resistivity, is given by P o = b/qP”(nob
+ Po).
(6)
Here no is the concentration of free electrons and p o is the concentration of free holes. Equation (5) shows that the spectral responsivity depends linearly on the applied electric field. In practice, an upper limit for the responsivity exists which depends upon the Joule heating produced in the sample by the applied basis. Expressing Eq. (5) in terms of Pn, the power dissipation per unit surface area, results in :#n,pc
=
qAP.[l
+ (1/~)1~PcP;/2w h~wd~‘~
(7)
In general, photoconductive detectors will be limited by thermal noise, u,,, , and/or generation-recombination noise, ug+. Because these add in
quadrature, the total noise voltage uT is given by
The expression for the thermal noise voltage is
where Ajis the electrical bandwidth within which the noise is measured, k is Boltzmann’s constant, and T is the absolute temperature. Because the form of the g-r noise expression depends upon the conditions under which the detector operates, the expressions appropriate to each condition will be introduced where needed.
2.
INDIUM ANTIMONIDE DETECTORS
43
The spectral detectivity D,* is given by
DA* =
( l ~ ) " ~ % ' ~ (' IA2 f ) VT
where Af is the noise bandwidth. and D,* expressions is In practice, the wavelength /z employed in the the long wavelength limit lo,which is related to the forbidden energy gap E, by /zo = hc/E,.
(11)
The spectral peak responsivity 9,0and detectivity D t are related to the 500°K blackbody values a(50WK) and D*(500°K) by
B(50WK) = 2I0G(500"K)
(14
D"(500"K) = D~oC(5000K),
(13)
and where the G function is defined by Kruse et aL44 Appropriate values of G(500"K) and loare listed in Table 111. TABLE 111 VALUES OF
a.
AND
~ ( 5 0 0 0FOR ~ ) INSB
AS
FUNCTIONS OF TEMPERATURE TemperaturevK) l o( p ) 300
6.6 6.0 5.2
195
I1
G(500"K) 2.8 3.9 5.7
a. Operation at Room Temperature have shown that the recombination process in p-type InSb Zitter et of moderate or high purity at room temperature is of the direct Auger type. Thus the electron and hole lifetimes are equal. The mobility ratio at room temperature, which can be determined from Figs. 8 and 9, lies between 60 and 105, depending upon purity. The expression for zpc, Eq. (2),thus becomes Zpc % 5,.
(14)
The dependence of zpc upon hole concentration in p-InSb at 300°K is shown in Fig. 18. 44
See Kruse et a ~ , ~p. '362.
44
PAUL W . KRUSE
The intrinsic concentration ni at room temperature is 1.6 x loi6~ m - ~ . Since ni2
= n o ~ 3o
(15)
the electrical resistivity po, Eq. (6),can be written as Po =
no Po d n o 2 p n + ni2pp) dni2pn + PO'CCJ
(16) '
From the dependences of pn and p p upon purity shown in Figs. 8 and 9 the dependence of p o upon no in n-type InSb and upon p o in p-type InSb at 300°K has been calculated (see Fig. 27). These data should be compared to Fig. 10, which relates to p-type material only. The data of Fig. 27 will be employed in the calculation of the responsivity and detectivity. From the dependence of tpC upon purity (Fig. 18) and the dependence of po upon purity (Fig. 27), the dependence of spectral responsivity upon purity can be determined from Eq. (7). The results of the calculation are illustrated
Id' 5 -
2 -
-
Id2-
I
v
f0 e
1
5 -
2-
lo3
-
5-
cn
z
(L
I-
2-
z 1.6
,041
I'
I
I
I
I
I
I
FIG.27. Dependence of resistivity po at 300°K upon majority carrier concentration in n-type and p-type InSb.
45
FIG.28. Dependence of spectral responsivity for photoconductive operation at 300°K upon majority carrier concentration in n-type and p-type InSb, assuming AD = 6.6 p, PD = 5 W/cmZ, d = l o p , and w = 1 mm.
in Fig. 28, assuming 1 = lo= 6.6 p (Table III), w = 1 mm, d = 10 p, and PD = 5 W/cm2. The dimensions are typical of photoconductive InSb detectors operating at room temperature. The maximum allowable value of the power dissipation obviously depends upon the manner by which the sensitive element is bonded to the heat sink ;the value of 5 W/cm’ is believed to be a representative one. Figure 28 shows that the optimum spectral responsivity of room temperature InSb photoconductive detectors is found in p-type material having free. theoretical hole concentrations of approximately 1 x 10’’ ~ m - ~The maximum value for the given values of thickness, width, and power dissipation per unit area is approximately 6 V/W at 6.6 p wavelength. Since the derivation of gA0 assumes complete absorption of the incident radiation and zero surface recombination velocity, values for real detectors will be substantially less. Determination of the spectral detectivity requires knowledge of the limiting noise mechanism. As stated previously, llf power-law noise will be neglected because no analytic expression exists for the amplitude of the noise
46
PAUL W . KRUSE
loi6
2
I
I
I
5
,017
2
5
MAJORITY CARRIER CONCENTRATION (CM-’I FIG. 29. Dependence of spectral detectivity for photoconductive operation at 300°K upon majority-carrier concentration in n-typc and p-type InSb, assuming lo= 6.6 p, P, = 5 W/cm2, d = l O j t , and w = 1 mm.
voltage. In any event, it has been established experimentally that roomtemperature InSb photoconductors are limited by thermal noise at all bias values below that at which excessive heating occur^.^^-^^ Thus the expression for the spectral detectivity [from Eqs. (5), (9), and (lo)] is Figure 29 illustrates the dependence of D t upon purity for n-type and p-type InSb at 300”K, assuming the same values of the parameters used for determining gA0 in Fig. 28. In contrast to the responsivity, the detectivity is relativeiy independent of purity for p-type samples in the range from intrinsic to 1 x lo” cmP3holes, achieving a slight maximum of 9 x lo8 cm Hz’’’/W at 7 x 1 O I 6 holes. As was true for the responsivity, the detectivity for
‘’ T. S. Moss, in “Photoconductivity 46 47
48
Conference” (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 427. Wiley, New York, 1956. G. H. Suits, W. D. Schmitz, and R. W. Terhune, J . A p p l . Phys. 27, 1385 (1956). R . E . J.KingandB.E.Bartlett, PhilipsTech. Reu.22,217(1961). D. G. Avery, D. W. Goodwin, and A. E. Rennie, J . Sci. Instr. 34,394 (1957).
2.
INDIUM ANTIMONIDE DETECTORS
47
n-type material is far less than for p-type of comparable purity. Again, real detectors will exhibit values of D,* well below the theoretical maximum. Two comments should be made with regard to Figs. 28 and 29. First, the derivations of BL0and OX, assume that the detector is operated in the opencircuit voltage condition, which is easier to realize experimentally than the short-circuit current one. Second, because no experimental information is available concerning the dependence of zpc on purity in n-type material, the calculations upon which Figs. 28 and 29'are based have assumed that dependence to be the same as in p-type material. In other words, the 300°K value of zpc for 1 x 1017cm-3 n-type InSb is assumed to be the same as that for 1 x 1017cm-3 p-type material. In general, the Auger lifetime for n-type semiconductors is less than or equal to that for p-type ones. Thus the values of gA0 and 0%in n-type InSb shown in Figs. 28 and 29 are upper limits. b. Operation at 77°K
The discussion in Section 3 , supported by Fig. 20, showed that in p-type InSb at 77°K the photoelectromagnetic response time zPEM is independent of purity. ZitterZ9 has shown that in general zpEM is given by ZPEM
= (z,
+ czp)/(f + c),
(18)
where c = noIP0.
In p-type InSb at 77°K c is much less than unity, because the intrinsic , less than the majorityconcentration, of the order of 10'' ~ m - is~ much carrier concentration in the purest samples. Thus in p-type InSb at 77°K 7pEM
= z,
=2 x
sec
(p-type),
(19)
where the value shown in Fig. 20 has been introduced. On the other hand, Fig. 20 shows that the photoconductive response time 7pcin p-type InSb at 77°K varies reciprocally with the purity. From Zitter's expression for zpc, Eq. (2), it can be seen that ZPC
= rplb = lC/P,b
(P-tYPe),
(20)
where b is no greater than 50 (see Figs. 6 and 7). Zitter et indicate IC = 1 x 109cm-3 sec, Laff and Fan33 state K = 1.5 x lo9 ~ r n sec, - ~ and G ~ o d w i nfeels ~ ~that K = 4 x lo8 cmP3sec is the most appropriate value. In n-type InSb the electron and hole lifetimes are equal to each other and independent of purity, having a value of 8 x sec (see the right hand 49
D. W. Goodwin, J . Phys. Chem. Solids 22,401 (1961).
48
PAUL W. KRUSE
side of Fig. 21). It is assumed that these data at 84°K also represent the data at 77°K. Thus zpc z 5, = zp = 8 x lo-’ sec (n-type). (21) Recombination in InSb at 77°K is by means of recombination centers, which Hollis et believe to be of a simple nature. Thus the appropriate recombination model is the Shockley-Read3, one. In the simplified case in which the density of recombination centers is low the Shockley-Read model requires the majority and minority carrier lifetimes to be equal to each other, given by T ~ where ~ ,
here T ~ and , T~ , , ~ are the minority carrier lifetimes when the Fermi level is at the conduction band edge or valence band edge, respectively, and n, and p1 are the electron and hole concentrations, respectively, when the Fermi level is at the recombination center energy level. Since the recombination mechanism in n-type InSb at 77°K is of the Shockley-Read type, and since the lifetimes are equal, Eq. (22) applies. From Eqs. (21) and (22) it can be seen that in n-type InSb at 77°K the expression for the Shockley-Read lifetime becomes
zSR z T ~ = ,8 x~ sec (n-type). (23) On the other hand, in the general case in which the recombination-center concentration is so high that it exceeds no, p o , nl,andp,, which amounts to exceeding the majority carrier concentration, then the majority and minority carrier lifetimes are unequal and Eq. (22) does not apply. Because the recombination mechanism at 77°K in p-type InSb is Shockley-Read, but the lifetimes are unequal, the recombination center concentration is large in that material compared to the majority carrier concentration for the range of hole concentrations considered by the various authors. Consider now the expression for the spectral responsivities of n-type and p-type detectors under conditions of similar doping and similar power dissipation. From Eqs. (6), (7), and (20) the spectral responsivity of p-type detectors at 77°K is given by T, = z p =
where it has been assumed that po 9 no&.From Eqs. (61, (7), and (21)
where it has been assumed that nob 9 po.
2.
I' 0 1(!13
49
INDIUM ANTIMONIDE DETECTORS
;
; ; 1;l5 ;
loo
MAJOR IT Y CAR R I E R CONCENTRATION ( C M-
FIG.30. Dependence of spectral responsivity for photoconductive operation at 77°K upon majority-carrier concentration in n-type and p-type InSb, assuming 1, = 5.2 p, Po = W/cm2, d = 5 p, and w = 1 mm.
Figure 30 illustrates the dependence of the spectral responsivity at the peak wavelength upon majority-carrier concentration in n-type and p-type InSb at 77"K, based upon Eqs. (24) and (25). Here it has been assumed that the peak wavelength ;lo is 5.2 p, that a power per unit area PDof 10- W/cm2 can be dissipated equally well by either type, that the detector width w is 1 mm, and that the thickness d is 5 p. Values for pn and b have been obtained from Figs. 6 and 7. For p-type InSb the value of IC = 1 x lo9 cmP3sec has been assumed to be the best compromise between the three reported v a l ~ e s . For ~ ~ n-type * ~ ~ InSb ~ ~ T, ~ = 8 x lO-'sec, as pointed out previously. From Fig. 30 it can be seen that the spectral responsivity at 5.2 ,u of p-type InSb detectors theoretically can be well above lo6 V/W. Again, much lower values will be obtained in practice. The values for n-type detectors can be seen to be about two orders of magnitude lower than for p-type at lOI4 cm-
50
PAUL W . KRUSE
majority carrier concentration. The discrepancy becomes even greater for samples of higher purity. Consider now the expressions for the spectral detectivity of n-type and p-type InSb detectors at 77°K. The appropriate noise mechanisms must first be determined. Again, llf power-law noise will be ignored. Since the recombination mechanisms differ in n- and p-type InSb at 77°K-two variants of the Shockley-Read mechanism-it follows that the g-r noise expressions also differ. In p-type InSb, for which the electron and hole lifetimes are vastly different, the density of recombination centers is much higher than the hole concentration. Since the electron concentration is many orders of magnitude below the hole concentration, the recombination centers are almost completely empty of electrons. Because the acceptor levels are completely ionized, the instantaneous concentration of free holes is governed by the generation and recombination rate fluctuations between the valence band and the recombination centers. Furthermore, the conductivity is totally dominated by the holes. Thus, as Van Vliet” shows, the proper g-r noise expression for p-type InSb at 77°K is that of excitation and recombination of a single type of carrier from a single type of center, i.e., Vg+ =
2ib‘T;’’R(Af) ”’/(polWd)
”’
(p-type),
(26)
where ib is the bias current. G ~ o d w i nhas ~ ~experimentally verified the application of this expression to p-type InSb at 77°K. In n-type InSb, however, a different expression applies. Here the electron and hole lifetimes are equal, although their concentrations differ greatly. Van Vliet5’ has shown that the appropriate expression is
Introducing Eq. (23) causes Eq. (27) to become
In n-type InSb thermal noise must also be considered. Combining Eqs. (6), (8), (9), and (28) results in the expression for the total noise voltage: VT
51
=
2ib(b + l)b(nop0)1’2~~iZ11/2(Af)1~zb b o b + ~ ~ ) + ~P ~ () ’ n~ ’ ~( W ~ ) ~ ~ ‘ ~ P ~
Van Vliet,43 Eq. (145), in which See Van Eq. (126).
T~
< T,, and n, 9 (po + pi).
2.
INDIUM ANTIMONIDE DETECTORS
51
Consider now the spectral detectivity of p-type detectors. From the general expression for the detectivity, Eq. (lo), the responsivity of p-type detectors, Eq. (24), the noise voltage of p-type detectors, Eq. (26), and the majority carrier lifetime in p-type material, Eq. (20), the spectral detectivity of p-type detectors at 77°K is found to be
Dk*= ( A / 2 h ~ p ~ ) ( ~ / d ) ' /(p-type). ~
(30)
On the other hand, the spectral detectivity of n-type detectors is, from Eqs. (lo), (21), (2.9, and (29),
where
Since in n-type InSb at 77°K no
+ p o , Eq. (31) becomes (33)
or
"(?!I
112
D,* = 2hcni d
(1 +
r)-li2
(n-type).
(34)
Equations (30) and (34) illustrate the major difference between p-type and n-type InSb photoconductive detectors operating at 77°K. In p-type detectors the spectral detectivity increases as the majority carrier concentration po is reduced. In n-type detectors the spectral detectivity increases as the majority carrier concentration is increased, provided that is much less than unity. This somewhat surprising behavior for n-type detectors arises because the g-r noise is reduced as the majority carrier concentration is increased [see Eq. (2811. In order to achieve the highest performance in n-type detectors, it is necessary to reduce r to well below unity, equivalent to requiring the g-r noise voltage to greatly exceed the thermal noise voltage. For n-type detectors for all reasonable values of purity, i.e., no > 10" ~ r n - the ~ , expression for r reduces to
r =kTno4w2d2qp, ib2ni2Tn Obviously,
(35)
r can be made small by going to high bias currents. However,
52
PAUL W. KRUSE
lo'2
5
1013 2
5
10'4 2
ELECTRON CONCENTRATION
5
,d5
no (CM-3)
FIG.31. Dependence of r upon majority-carrier concentration no in n-type InSb at 77"K, assuming ni = 1 x 1 0 " ~ m - ~cn, = 8 x lO-'sec, d = 5 p , and Po = W/cm'.
above some threshold value of power dissipation, excessive heating will occur. In terms of power dissipation per unit area PD,Eq. (35) becomes
Figure 31 illustrates the dependence of I7 on majority carrier concentration no in InSb at 77"K, assuming n, = 1 x 10'' ~ r n - z~, , = 8 x lO-'sec, d = 5 p , and PD = lop3W/cm2. It can be seen that at this power dissipation, for all reasonable values of purity, r is never small compared to unity. In this event Eq. (34) reduces to
2.
53
INDIUM ANTIMONIDE DETECTORS
t t
a
3
c'
I
N
I
I 0 * r0
n
> k i
1
I0 W IW
n 2
U
BLIP LIMITPHOTOCONDUCTIVE MODE ; 300.K BACKGROUND; 2 7 1 STER. FOV; A. 5.2pM
2t
u
FIG. 32. Dependence of spectral detectivity for photoconductive operation at 77°K upon majority-carrier concentration in n-type and p-type InSb, assuming lo = 5.2 p, ni = 1 x 10” W/cm2. ~ m - 7,~ =, 8 x IO-’sec, 1c = 1 x lo9 sec, d = 5 p, and Po =
Consider now the relative values of spectral detectivity for p-type and n-type detectors, Eqs. (30) and (34). The values at the peak wavelength of 5.2 p are illustrated in Fig. 32, assuming the values of the parameters listed above and IC = 1 x lo9 cm-3 sec. Over the entire range of majority-carrier concentration shown, from 1 x 10” cm-3 to 1 x 1015~ r n - the ~ , detectors offer equivalent performance. However, the photon noise limit (BLIP) for a 300°K hemispherical background imposes an upper limit at a value of D t ( 5 . 2 ~of) about 1.2 x 10” cm H Z ~ J * / W Thus , ~ ~the higher responsivity of the p-type detector provides the decisive advantage in most applications. Were it possible to increase PD over the chosen value, n-type detectors would offer the higher detectivity, making them superior to p-type when operated under reduced background conditions. 5z
See Kruse et
p. 360.
54
PAUL W . KRUSE
c. Operation at 195°K As discussed in Section 3, Wertheirn3O found the recombination mechanism in both n-type and p-type InSb in the range from 130°K to 250°K to be of the Shockley-Read type. These results were confirmed by Zitter, Strauss, and Attard3’ for p-type InSb, and Nasledov and S m e t a n n i k ~ v for a ~ ~both n-type and p-type material. Wertheim found that the Shockley-Read lifetime, Eq. (22), reduced to
+ PO)
(37) was found to be constant over for both n-type and p-type material, where tp,O . =~ ~ the temperature range studied. According to Zitter et ~ 1 zp,o 8x sec. On the other hand, the data of Hollis et aL3’ indicate a value sec. in the range 4.0-5.5 x The photoconductive response time at 195”K, obtained from Eqs. (2) and (37), is therefore zSR =
zn = z p = z p , O n O / ( %
~ P = C 7, =
zp =
zSR
= zp.ono/(no
+
PO).
(38)
Assuming again that the limiting factor is the allowable power dissipation, the spectral responsivity is found from Eqs. (7) and (38) to be
In terms of the intrinsic concentration ni, the spectral responsivity, from Eqs. (16) and (39), is
or
Figure 33 depicts the dependence of the spectral responsivity at 195°K upon majority carrier concentration, based upon Eqs. (40)and (41). The value of n,, from Fig. 2, is 1 x 10’’ ~ m - From ~ . the data of Hollis et al.35 a value for zp,o of 5 x sec has been selected. The wavelength Lo at . value of PD is which the spectral response peaks at 195°K is 6 . 0 ~ The assumed to be lo-’ W/cm2. Values of thickness d and width w are assumed to be 10 p and 1 mm, respectively. Values of pn and p p at 195°K as functions of sample purity have been taken from Fig. 5. Figure 33 shows that the optimum purity for maximizing the responsivity is slightly p-type, about 2 x ~ r n - The ~ . responsivity remains reasonably
2.
55
INDIUM ANTIMONIDE DETECTORS
5 x lo2
2
;
Ioo 21 0 ' ~
2
5
10'6
2
5
10'~
FIG.33. Dependence of spectral responsivity for photoconductive operation at 195°K upon majority-carrier concentration in n-type and p-type InSb, assuming I , = 6 . 0 ~ PD . = lo-' W/cmZ, d = 10 p , and w = 1 mm.
high to about 5 x 10'5cm-3 p-type, but then falls off precipitously. The responsivity for n-type samples falls off rapidly with decreasing purity. Consider now the appropriate noise expression. Again, llf power law noise will be ignored. Because the recombination mechanism is ShockleyRead, with both lifetimes equal in both n-type and p-type material, the proper g-r noise expression is the same as in n-type InSb at 77°K. In other words, Eq. (27) properlj. describes g-r noise in both n-type and p-type InSb at 195°K. Introducing the expression for z ~ Eq. ~ (37), , gives rise t o
Expressing the resistance R in terms of the carrier concentrations and mobilities, and including the expression for the thermal noise voltage
56
PAUL W. KRUSE
[Eq. (9)], gives the expression for the total noise voltage in n-type and p-type InSb at 195°K : 2ibnop~/zb(b + l)11~2~~!~(Aj)1'z (no + po)(bn0 + p o ) 2 ~ ~ . ~ 3 / 2 d 3 / 2 kT(no po)'(bn0 p o ) 3 q p . ~ 2 d 2 1/2 x [I+ (43) i,2n02pob(b 1 ) 2 ~ p , o Combining Eqs. (lo),(39), and (43) results in the expression for the spectral detectivity : VT
=
+
+ +
1.
or
where
or
As was true for n-type InSb at 77"K, the value of DA*at 195°K is maximized by causing A to approach zero by employing high bias currents. Figure 34 illustrates the dependence of A on majority carrier concentration in InSb a t 195"K, assuming n, = 1 x 10'' cmP3, d = lop, PD = lo-' W/cmZ, and tp,O = 5 x lo-' sec. The value of b, determined from Fig. 5, is approximately 80 for the concentrations of interest. Figure 34 shows that A is small in intrinsic material, but becomes important in n-type material at majority carrier concentrations greater than about 2 x 10lscm-3, and in p-type material for concentrations greater than about 5 x 10'scm-3. The value of DA* at A,, = 6.0 p is illustrated in Fig. 35, assuming the same values of the parameters given above. Whereas the maximum responsivity is found in p-type material, the maximum detectivity is found in n-type, because the g-r noise in n-type material is less than that in p-type. The maximum detectivity is found at an electron concentration of about 2 x 10l5 cm- '. For material somewhat less pure the detectivity decreases rapidly
2.
INDIUM ANTIMONIDE DETECTORS
,C?l
I
,o15
2
I 5
l
I
lo16 2
l
s
l
I
,017 2
s
l
57
MAJORITY CARRIER CONCENTRATION (CMm3)
FIG.34. Dependence of A upon majority-carrier concentration in InSb at 195"K,assuming T , , ~ = 5 x lO-'sec, ni = 1 x 1015~ m - PD ~ = , lo-' W/cm2, d = lop, and w = 1 mm.
with increasing carrier concentration as thermal noise becomes dominant. Even at the optimum carrier concentration the photon noise limit is not attained.
5. PHOTOELECTROMAGNETIC EFFECT The other photoeffect to be considered is the photoelectromagnetic, or PEM, effect. As stated in the introduction, PEM detectors have been designed only for operation at room temperature. When cooled, they offer no advantage over photoconductive or photovoltaic ones, and suffer the cooling problems associated with the use of the magnet. Thus the analysis of the PEM effect will be confined to only room temperature operation. As was true for the analysis of the photoconductive effect, the analysis of the PEM effect begins with the expression of ZitterZ9for the short-circuit
58
PAUL W . KRUSE
P
-I-I= - o [l 2l
Id"
22
,ne
l0lS
5
2
2
,016
5
10"
MAJORITY C A R R I E R CONCENTRATION ( C M - 3 )
FIG.35. Dependence of spectral detectivity for photoconductive opcration at 195°K upon majority-carricr concentration in n-type and p-type InSb. assuming 1, = 6 . 0 p z,,,~ = 5 x l o - ? sec, n, = I x l o t 5~ r n - ~P,,, = 10 W/crn2. and d = lop.
current per unit sample width, jS,PEM
=
4N&BLD*[1
+
5
(48)
where B is the magnetic induction and LD*,the effective ambipolar diffusion length in the magnetic field, is given by
+
+
Here c = n,/po, and z ~ E M= (7, C T ~ ) , / ( ~ c) as in Eq. (18). Because the recombination process at room temperature is of the direct Auger type, the
2.
59
INDIUM ANTIMONIDE DETECTORS
electron and hole lifetimes are equal. Thus TpEM = 7, =
(50)
zp.
Comparing this to Eq. (14), it can be seen that the PEM and photoconductive response times for InSb at room temperature are equal. Thus zpEMdepends upon hole concentration in p-InSb at 300°K in the same manner as zpc does, as illustrated in Fig. 18. The open circuit voltage v ~ is given , by~ ~ ~ UO,PEM
=
iS.PEMWRB
(51)
9
where w is the sample width. Here R B represents the resistance of the sample in the magnetic field, given by RB = (PB/PO)(POl/Wd)
(52)
9
and
+ c)/b(bc + l)] P B - 1 + j.if12B2[(b _ 1 + j.if12B2[(1 ~)/(1+ bc)]' PO
(53)
is the magnetoresistivity ratio. The dependence of the magnetoresistivity ratio upon majority-carrier concentration in InSb at 300°K is illustrated in Fig. 36. The intrinsic concentration, needed to determine c as a function of majority-carrier concentration, is 1.6 x l O I 6 cm-3. Values for the mobility ratio b, which lies between 60 and 105, depending upon purity, can be determined from Figs. 8 and 9. The magnetic induction B is assumed to be
l0l6
2
5
10'~
2
5
id8
MAJORITY CARRIER CONCENTRATION ( C M - 3 )
FIG. 36. Dependence of magnetoresistivity ratio upon majority-carrier concentration in InSb at 300"K, assuming ni = 1.6 x 10l6~ r n and - ~ B = 7000 G.
60
PAUL W. KRUSE
0.7 Wb/m2 (7000 G), a value attainable in the small magnets employed for InSb PEM detectors. Figure 36 shows that the magnetoresistivity ratio has its maximum value of approximately 2.5 in p-type InSb having a hole concentration of about 7 x 10'6cm-3, a conclusion supported by the data of Fig. 11. Figure 27 shows that p o , the resistivity in the absence of the magnetic field, also attains its maximum value in p-type material of slightly higher hole concentration. Thus the maximum resistance in the magnetic field is found in p-type InSb having a hole concentration of approximately 1 x lo" cm-'. Consider now the spectral responsivity BA.Because N is given by Eq. (3), N = H,rl/hcEw, the expression for BAis therefore
The dependence of W Aupon majority-carrier concentration according to Eq. (54) is illustrated in Fig. 37. Here it has been assumed that B = 7000 G, Lo = 6.6 p, w = 1 mm, and d = 20 p. Values of pn as a function of purity are those of Fig. 8. The dependences of p o and p B / p o upon purity are taken
10-2
9
,o'6
2
5
(0'7
2
5
2
5
MAJORITY CARRIER C O N C E N T R A T I O N (CM-3)
FIG.37. Dependence of spectral responsivity for PEM operation at 300'K upon majoritycarrier concentration in n-type and p-type InSb, assuming A, = 6.6p, B = 7000G, and d = 20p.
2.
INDIUM ANTIMONIDE DETECTORS
61
from Figs. 27 and 36, respectively. The dependence of z~~~ upon purity in p-InSb is the same as that of zpc (see Fig. 18). It has been assumed that 7pEM depends upon electron concentration in n-InSb in the same manner as it does upon hole concentration in p-InSb. Figure 37 shows that the highest responsivity is found in p-type InSb ~ . the assumed values having a hole concentration of about 8 x 1 O I 6 ~ m - For of the parameters, the highest value of spectral responsivity is approximately 5V/W. By comparing this with data on the room temperature photoconductive detector (see Fig. 28) the optimum purities for the two modes are seen to be approximately equal. The maximum responsivity for the PEM detector is slightly less than that for the photoconductive detector, based upon the assumed values of magnetic induction of 7000G and electrical power dissipation of 5 W/cm2. The spectral detectivity of the room temperature PEM detector can be calculated, based upon a thermal-noise mechanism, the only one operable in the absence of electrical bias. Here the appropriate resistance is that in the magnetic field. Thus Eq. (9) is modified to become
The expression for the spectral detectivity Da* determined from Eqs. (lo), (54), and ( 5 5 ) is thus
Note that high values of resistivity and magnetoresistivity ratio are desirable for maximizing Da*. Figure 38 illustrates the dependence of D,* upon majority carrier concentration from Eq. (56).The values of the parameters assumed are the same as those above. The highest spectral detectivity is found in p-type material having a hole concentration of approximately 7 x loi6~ m - The. ~ . maximum detectivity value is about 6 x lo8 cm Hz’/’/W. Comparing again the photoconductive mode (Fig. 29) with the PEM mode (Fig. 38), the optimum purity is found in each instance in p-type ~ concentration. For the material of approximately 1 x l O ” ~ m - hole assumed values of electrical power dissipation and magnetic induction the photoconductive mode appears slightly superior. It should be borne in mind that the calculations are based upon measurement of the open-circuit voltage, which is proportional to the resistance. If instead the short circuit current were measured, the optimum purity would no longer be near that which gives rise to the maximum resistance, but would be expected to be near or equal to the intrinsic value.
62
PAUL W . KRUSE
1
l0l6
2
5
I
I
1
2
5
2
3
MAJORITY C A R R I E R CONCENTRATION ( C t ~ l - ~ )
FIG. 38. Dependence of spectral detectivity for PEM operation at 300°K upon majoritycarrier concentration in n-type and p-type InSb, assuming I , = 6 . 6 ~B ~ = 7000G, and d = 20u.
IV. Preparation of Photoconductive and PhotoelectromagneticDetectors The previous part considered the theoretical aspects of the performance of photoconductive and photoelectromagnetic InSb detectors. This part will present details of the method by which the detectors are prepared, and the next will consider the experimentally realized performance, contrasting it to the theoretical predictions. The preparation of detectors can be divided into three major categories : (1) purification and crystal growth, (2) fabrication of the sensitive elements from the crystals, and (3) design of the housing into which the elements are placed. It is not the intent of this part to dwell in detail on any of these aspects, since the growth and fabrication aspects are standard methods employed in semiconductor technology, and the housing design is straightforward. Therefore each of these shall be discussed only in moderate detail.
2.
INDIUM ANTIMONIDE DETECTORS
62
6. PURIFICATION AND CRYSTAL GROWTH
The preparation of high purity single crystals of InSb has been reviewed by many authors, for example, L i a ~ ~ Hulme g , ~ ~and M ~ l l i nand , ~ ~Hulme.7 Commercially available, high purity (six nines) indium and antimony are reacted above the compound melting point of 523°C to form InSb. Because the partial pressures of indium and antimony are low, the reaction can proceed at atmospheric pressure. A reducing atmosphere is employed to prevent formation of indium and antimony oxides which react with the quartz ampoule. Horizontal zone refining of the compound in a reducing atmosphere is employed to remave foreign atom impurities, the dominant ones, as H a r m a showed, ~ ~ ~ ~ being zinc, an acceptor having a segregation coefficient greater than unity, and tellurium, a donor having a segregation coefficient less than unity. Because that of the latter differs only slightly from unity. zone refining to remove Te is tedious. Indium antimonide which has been extensively zone refined is n-type. The ionization energies of nearly all the foreign atoms, Ge excepted, are sufficiently small for the atoms to be ionized at 77°K and above (see Table I). Most workers have attributed the residual donor to Te, believing that deviations from stoichiometry are negligible. However, H ~ l m ereferring ,~ to Stocker’s datas6 on indium vacancies, considers the residual donor to be a lattice defect. Although the early photoconductive detectors of Frederikse and Blunt4 were n-type, and n-type detectors operating at 77°K theoretically are equivalent to p-type (see Fig. 32), normal practice is to prepare p-type ones because of their higher responsivities, which make them more easy to use. Thus it is necessary to compensate the residual donor, usually with zinc or cadmium, to form p-type material. Hole concentrations in the 10” cmrange at 77°K can be attained in this manner.57 Because the 300°K photoconductive and photoelectromagnetic detectors exhibit optimum detectivity and responsivity when slightly p-type, zinc or cadmium doping is also employed for them.57 Published information is lacking on the dopant for the 195°K photoconductive detectors. Because the optimum purity is only slightly n-type, it is probable that intrinsic material is used. In order to minimize the compensation problem in the high puritj material required for the 77°K photoconductive detectors, the use of the
’
S. C. Liang, in “Compound Semiconductors” (R. K. Willardson and H. L. Goering, eds.), Vol. I, Preparation of 111-V Compounds, p. 227. Reinhold, New York, 1962. 5 4 K. F. Hulme and J. B. Mullin, Solid-Srare Electron. 5,21 I (1 962). 5 5 T. C. Harman, J . Electrochem. Soc. 103, 128 (1956). 5 6 H. J. Stocker, Phys. Rev. 130, 2160 (1963). ” T. J. Davies. nersonal communication 53
64
PAUL W. KRUSE
deep acceptor germanium has been explored. Because germanium acceptors are deionized at 77°K due to their midgap position (see Table I), they can be introduced in a concentration sufficient to compensate the residual donors at a concentration much higher than is possible with a shallow acceptor. Single crystals of InSb are formed from the zone-refined polycrystalline ingots either by the Czochralski method or by zone leveling. Where attaining compensation is a problem, the zone-leveling approach is preferred for the greater yield of useable material.s7 As in the zone-refining process, growth is accomplished in a reducing atmosphere in a quartz ampoule or boat. Hulme and M ~ l l i nshowed ~ ~ that a faceting effect exists in which the segregation coefficients of selected impurities depend upon the growth axis. To minimize the faceting effect, growth along the [ill], and [lo01 axes should be avoided; acceptable axes are (311) and (1 10). Routine evaluation of the single crystal InSb is accomplished in several ways. Thermoprobing reveals the n- and p-type regions. The majority carrier concentration and mobility are established through measurement of the Hall coefficient and resistivity. An etch pit count reveals the dislocation density. By evaluating samples at selected intervals along the crystal, a “profile” or “map” is established which indicates the regions from which the sensitive elements should be selected.
[in]
7. FABRICATION OF THE
SENSITIVE
ELEMENT
In its final form the sensitive element consists of a thin InSb layer with attached electrical leads mounted on an electrically insulating substrate. The steps in preparing the element from the single crystal of InSb are discussed below. Because the process may differ in detail from one manufacturing group to another, the steps should be considered typical rather than unique. Except where noted, the processing details for photoconductive elements and photoelectromagnetic elements are the same. The single crystal of InSb which galvanomagnetic measurements have revealed to have the desired electrical properties is mounted on a ceramic block with quartz cement. Transverse cuts by means of a diamond saw or a wire saw are used to remove slabs 1-2 mm thick. The wire saw, preferred because it introduces less damage to the crystal, employs a slurry of glycerine and Sic to lubricate the wire. Each slab is degreased in warm trichloroethylene, rinsed in warm methanol, and dried by means of a nitrogen gas jet. Each slab is then lapped on silk with 600 mesh Sic, rinsed, lapped with lo00 mesh Sic, and rinsed again. At this point the processing of the photoconductive elements differs from that of the photoelectromagnetic elements.
2.
INDIUM ANTIMONIDE DETECTORS
65
Whereas photoconductive detectors require a low surface-recombination velocity on both the front surface (upon which the radiation is incident) and the back surface, photoelectromagnetic detectors require a low recombination velocity on the front surface and a high recombination velocity on the back. * Since lapping leaves the surface with a high recombination velocity, the back surface of the PEM detector is not etched in the manner described below. To prepare the front surface of the PEM detector and both surfaces of the photoconductive detector for etching, the surfaces are lapped to a mirror finish with a 0.1 p alumina powder. No scratches should be visible to the naked eye. After again cleaning the slabs thoroughly, they are etched in a mixture of equal volumes of undiluted HF. H N 0 3 , and CH3COOH. The etchant is rinsed away with distilled water and the slabs are dried in a nitrogen jet. Next the slabs are epoxied to substrates. The requirement which the substrate for a 300°K photoconductive or photoelectromagnetic detector must meet is that of sufficiently high resistivity in the event that the electrical contacts inadvertently touch the substrate. This is minor; the usual substrate material is glass in the form of a microscope slide. The photoconductive detectors operating at 195°K and 77°K not only impose more severe requirements on resistivity, but have the additional one of a thermal expansion coefficient which is in reasonably close agreement with that of InSb. For these reasons the usual choice of substrate for the cooled detectors is either high resistivity Ge or Irtran 2. To prepare the slabs for the “dicing” operation in which they are serrated into the individual detector elements, a protective coating of polystyrene dissolved in toluene is applied to the exposed surface and allowed to become firm but not hard. The slabs are then cut into “rectangles,” i.e., rectangular parallelepipeds, having dimensions sufficient to allow for placement of the electrical contacts. Each rectangle is etched in the etchant again until the desired final thickness is attained. For the 300°K photoelectromagnetic detector the optimum thickness is about 2 5 p , whereas that for the 300°K photoconductive element is 5-10 p. The optimum thicknesses for the 195°K and 77°K photoconductive elements are also about 25 p. Platinum wire electrical contacts are applied to the sensitive elements by means of indium solder. For better delineation of the sensitive area the indium is evaporated onto the sensitive elements and the platinum leads applied by thermocompression bonding. An underlying evaporated gold layer is sometimes employed for better bonding. Figure 39 illustrates the final form of the photoconductive or photoelectromagnetic sensitive element.
’’See Kruse et
(Chap. 9).
66 PAUL W . KRUSE
tn c W
W
d
-
b c:
FIG.40. lnSb four-element array. (After Williams.60)
Q
a
(L
C
n
v)
I
w
t t
2
cn
v)
w
0
L
FIG. 39. Final configuration of sensitive element.
2.
INDIUM ANTIMONIDE DETECTORS
67
An alternative approach to the use of a wire saw for removal of the sensitive elements from the slab employs photolithographic technique^.^^ Here the slab is mounted on a turntable rotating at 1500rpm, and 3-4 drops of KMER (Kodak Metal Etch Resist) are placed on the center of the slab. Radial forces spread the KMER in a uniform film over the slab. The coating is allowed to dry at room temperature, then baked at 80°C. The KMERcoated slab is then dipped in KPR (Kodak Photo Resist), allowed to dry, then baked at 80°C. The KPR-KMER-coated slab is then exposed to a high intensity ultraviolet-rich radiation source through a mask whose transparent and opaque regions correspond to the geometrical requirements of the sensitive element. Since the KPR-KMER coating when exposed to ultraviolet radiation becomes resistant to the subsequent chemical etching solutions, the mask pattern should allow radiation to fall on the coating overlying the desired shape of the sensitive element and block radiation from falling in those regions where it is desired to serrate the elements. The coating is then developed by spraying it with KPR developer, flushed with distilled water, sprayed with KMER developer, and again flushed with distilled water. The remaining coating, overlying those areas which it is desired to protect from etching, is then baked at 80°C. The HF-HN0,-CH,COOH etchant is then applied to remove the unprotected areas of InSb. A wire saw is then employed in the etched regions to serrate the substrate as desired. This photolithographic method is of great value for the formation of multielement arrays of complex shapes on a common substrate. An example of a four-element photoconductive array6’ is illustrated in Fig. 40. 8. DETECTOR HOUSINGDESIGN
The housings, mountings, or envelopes of the InSb detectors fall into three categories : those for the 300°K photoconductive detector, those for the 195°K and 77°K photoconductive detectors, and those for the 300°K photoelectromagnetic detectors. Details of the designs will vary according to the manufacturer and application ; what is presented here can be considered to be typical. CI.
300°K Photoconductive Detector
The term “housing” for the 300°K photoconductive detector is a misnomer; the sensitive element is simply mounted on a copper block which also serves as a heat sink (see Fig. 41). Because of the low resistivity of InSb 5y
6o
For further information, see Introduction to Photofabrication Using Kodak Photosensitive Resists, Kodak Industrial Data Book P-79, Eastman Kodak Co., Rochester, New York ( 1967). D. B. Williams. Injrared Phys. 5, 57 (1965).
SAPPHIRE WINDOW
I n S b SENSITIVE ELEMENT
I-& O T!/
I n S b ELEMENT
AL UMI FORM N IZ EFOV D INTERIOR LIMITING APERTURE
SOLDER CONTACT TO ELEMENT AND LEAD
COPPER MOUNTING
SILVER PAIN LEADS
! M
r K O V A R RINGS
? w
P
sm
FINAL SEAL HELIARC WELDSPACE FOR COOLANT
FIG.41. Mounting for 300°K photoconductive detector. (After King and Bartlett.47)
FIG.42. Dewar for 195°K and 77°K photoconductive detectors. (After Kruse et ~ 1 . ~ ' )
2. INDIUM
ANTIMONIDE DETECTORS
69
56°AVERAGE FIE1.D-OF-VIEW
/
\ 3 . 5 - 5 . 0 ~SPECTRAL BANDPASS FILTER
COLD SHIELD ASSEMBLY
FIG. 43. Dewar for 77°K four-element array photoconductive detector incorporating background limiting cold shield and filter. (After Williams.60)
at 300"K,it is desirable to have a long, narrow element if the application will allow it. A problem with this design is the lack of protection for the sensitive element. b. 195°K and 77°K Photoconductive Detectors
The housing design for the 195°K and 77°K detectors shown in Fig. 42 is basically a vacuum Dewar, the coolant dry ice or liquid nitrogen being contained within the central well. The sensitive element (see Fig. 39) is mounted on the interior (vacuum) surface of the well, viewing the surroundings through a sapphire window. The interior surface of the external wall of the Dewar is aluminized to minimize coolant loss. The reflecting properties of this surface, together with those of an annular aluminized ring on the sapphire window, provide a limitation to the field of view of the detector which increases the background photon noise limited detectivity. Electrical leads, which can be either silver paint or wires embedded in glass, run along the interior surface of the sensitive well to Kovar pins penetrating the glass. Kovar weld rings are employed to ease assembly problems. A more complex design employed with a four-element array reported by Williams6' is shown in Fig. 43. Here a cold shield assembly is provided in the form of an interior cap over the array having an aperture which defines the field of view to 56", thus increasing the background photon noise limited detectivity62by a factor of approximately two. A 3.5-5.0 p spectral bandpass filter mounted over the aperture provides an additional enhancement in the detectivity by rejecting background photon noise outside of the 3.5-5.0 p interval. The Dewar design requires five electrical leads, one to each element and one common to all. 6 1 See Kruse et Chap. 10. "See Kruse et ~ f . , ~Fig. ' 9.13.
70
PAUL W . KRUSE
HIGH PERMEABILLTY
POLE PIECES
BRASS MOUNTING PLATE
I n S b SENSITIVE EL EMENT BRASS CASE
BRASS BASE PLATE TWO- PIN SHIELDED
CONNECTOR
FIG.44.Housing for 300°K photoelectromagnetic detector. (After Kruse
ct
db1)
c. 300°K Photoelectromagnetic Detector The housing design of the 300°K photoelectromagnetic detector (Fig. 44) incorporates an Alnico V U-shaped permanent magnet within a brass case.61 High permeability pole pieces direct the magnetic flux through the sensitive element. The requirement for a high flux density within the sample restricts the sample width to a value of about 1 mm or less in order that the pole piece separation not be excessive. As was true for the 300°K photoconductive detector, it is desirable to have a long, narrow sample if the application allows in order to have a high resistance and responsivity. A CaF, infrared transmitting window is mounted within the brass case, which incorporates a two-pin shielded electrical connector. Obviously, the photoelectromagnetic detector is much more bulky than the 300°K photoconductive one ;however, the sealed housing of the former affords far more protection for the sensitive element. V. Performance of Photoconductive and PhotoelectromagneticDetectors
Part I11 analyzed theoretically the performance of InSb photoconductive and photoelectromagnetic detectors. In this final part the actual measured performance of detectors is compared to the theoretical predictions. It would be most desirable to present data on detectivity and responsivity as
2.
INDIUM ANTIMONIDE DETECTORS
71
functions of purity for each of the temperatures and modes of operation, in order to determine whether the experimental points fall along the theoretical curves. Unfortunately, such data are not available in the literature. Instead, this part will present performance data on detectors which are assumed to be prepared in an optimum manner. The data fall into two categories. First, the performance of a single detector for each operating mode and temperature will be reported. The data on this representative detector will include spectral detectivity, frequency response, noise spectrum, frequency dependence of peak spectral detectivity, and, for the photoconductive mode, signal and noise as functions of bias current. The spectral detectivity, spectral responsivity, and response time values will be compared to the values predicted in Part 111. Second, information will be presented on the statistical distribution of the values of detectivity, response time, and resistance of a large number of 77°K photoconductive detectors made using supposedly identical processing parameters. Information of this type is especially valuable for systems requiring multielement arrays, where uniformity is of paramount importance. It would be desirable to have similar information on detectors operating at 300°K and 195°K;such information is not available in the literature. 9. PROPERTIES OF SELECTED HIGHPERFORMANCE AND PHOTOELECTROMAGNETIC DETECTORS
PHOTOCONDUCTIVE
The selection of data which truly represent high performance state-of-theart detectors is difficult. The available sources include manufacturers’ specifications and published literature. With either of these the accuracy and completeness of the data may be areas of concern. One source of information stands above all, namely, the reports of the Infrared Division, U.S. Naval Ordnance Laboratory Corona, Corona, California (now the Infrared Technology Division of the Naval Electronics Laboratory Center, San Diego). This facility, formerly part of the National Bureau of Standards, has been measuring the performance of infrared detectors supplied to it from worldwide sources for approximately two decades. The data are presented periodically in so-called “NOLC Reports.” By employing a standard format, the reports allow an easy comparison between detectors. There are two problems connected with the use of the NOLC reports, namely, military security and information selection. It was obviously necessary to choose only unclassified data for presentation herein. This is not a serious problem for the InSb detectors, since much of the data are unclassified. In reviewing the data it was necessary to select one set for each operating mode and temperature which best represented the state of the art. This is a subjective judgment with which it is hoped most readers will agree.
72
PAUL W . KRUSE
TABLE IV PROPERTIES
OF
SELECTED DETECTORS" ~
~
~~
Detector 300°K Photoconductive
300°K Photoelectromagnetic
195°K Photoconductive
5.5
5.4
1.9 x 10'
1.7 x lo*
5.9
1.9 x 10'
1.7 x 10'
8.6 x lo9
6.5 x 10"
7.1 x 107
5.8 x lo7
1.5 x 109
7.5
109
1.96
1.1
140
1.1
105
35
1.9
104
0.7
0.38
flat 1.01 x 0.1
> 75 0.128 x 0.106
109
5.16 x
41
60
(wc)
1. Thus the agreement between the NOLC data and the calculations based upon the simplifying assumptions is felt to be reasonable. 1 1 . STATISTICAL DISTRIBUTION OF THE PROPERTIES OF LARGENUMBERS OF 77°K PHOTOCONDUCTIVE DETECTORS
Lennard64 has presented in histogram form the statistical spread in the properties of 100 InSb photoconductive detectors operating at 77°K. Williams6' has presented statistical data on an additional 74 detectors in the form of four-element arrays which operate in the photoconductive mode at 77°K. These data are discussed below. 64
J. K. Lennard, unpublished work (1964).
78
PAUL W. KRUSE
t-
u w
301
THEORETICAL BLIP L I M I T SPECIFIC DETECTIVITY
20
CI
I ‘\
m
z
0.9
1. I
1.3
I .5
I .7
2. I
1.9
D ” ( ~ O O O K ,iooo,i,go~),( IO’OCM HZ”*/WATT)
FIG. 50. Histogram of blackbody detectivities of 100 77°K-photoconductive detectors. (After Lennard.h4)
According to Lennard,64 the 100 photoconductive detectors were produced by the same manufacturing techniques, all having a sensitive.area of 0.5 x 0.5mm2 and a 90” field of view. The detectors were individually mounted in Dewars similar to that illustrated in Fig. 42. Histograms of the detectors’ properties are displayed in Figs. 5@-52. That of Fig. 50 represents the values of D*(50O0K,1000,1), obtained by rounding off the measured values to two significant figures and adding the number of occurrences of a given detectivity value. As indicated in Table 111, the values of DL*(5.2p,
A ,
/
I I
\
,‘\
\
/
4
6
L 12
8
PHOTOCONDUCTIVE TIME CONSTANT
10 (p
SEC 1
FIG.S1. Histogram of photoconductive response times of 100 77°K photoconductive detectors. (After L e n n i ~ r d . ~ ~ )
2.
79
INDIUM ANTIMONIDE DETECTORS
DETECTOR RESISTANCE (OHMS
I
lo3)
FIG. 52. Histogram of resistance values of 100 77°K photoconductive detectors. (After Lennard.64)
1000,l) can be obtained by multiplying the D*(500°K,1000,1) values by 5.7. The most probable value of DA*(5.2p,1000,1)can be seen to be approximately 7 x 10" cm Hz'/'/W. The distribution in photoconductive response times is illustrated in Fig. 51; the most probable value is 8psec. Finally, Fig. 52 illustrates the distribution in resistance. A value of 4000 ohms per square is most probable. TYPE 1
I
- I6 DETECTORS
SIN
TYPE
P
- 47 DETECTORS
SIN
BOO- IOOOp AMPS
0
300 500 BIAS CURRENT, *AMPS
TYPE m-I0 DETECTORS SIN
0
300 BIAS CURRENT,
500 p
AMPS
I
1 1
0
300
500
BIAS CURRENT, p AMPS TYPE
IX - 25
DETECTORS
SIN
BIAS CURRENT, p AMPS
FIG.53. Dependences of detectivity (proportional to SIN) upon bias current for 77°K photoconductive detectors. (After Lennard.64)
80
PAUL W . KRUSE
P.C.InSb SPECIFIC SPECTRAL RESPONSE AFTER INCORPORATION OF 3.5 5 . 0 ~COLD FILTER AND 56’ FIELD-OF-VIEW DEFINING
\
2.01
\
-
WAVELENGTH FOR PHOTOCONDUCTOR WITH 180’
SPECIFIC SPECTRAL
2.0
3 0
40
5,O
6.0
WAVELENGTH ( p )
FIG.54. Average spectral detectivity of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)
Lennard64 also found that the dependence of the detectivities upon bias current fell into the four categories illustrated in Fig. 53. The optimum bias current range common to all except the 25 categorized as Type IV was
*O v)
t
W I T H 180’ UNOBSCURED FIELD-OF- VIEW V I E W I N G A 56. BACKGROUND
t
I5 w
S P E C T R A L BANDPASS FILTER
+ W
n LL
0
10
a
w m
s 5 2
0 0.8
1.0
1.2
1.4
1.6
1.8
D“(500.840.11~10-lo(CM
2.0
2.2
HZ”*/WATT
2.4
2.6
1
FIG.55. Histogram of blackbody detectivities of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)
2.
INDIUM ANTIMONIDE DETECTORS
n
81
0 180' UNOBSCUREO FIELO-OF-VIEW 1 3.5 - 5.0 + BANDPASS FILTER 56* AVERAGE FIELD -OF-VIEW
W
I-
W 0
W
L
i 0.8
0.4
1.0
1.2
I
i.4
1.6
18
2.0 2.2 2.4 2.6
D: (4.6p,840,1) x IO-"(CM H Z 1 ' h A T T )
FIG.56. Histogram of 4.6 p spectral detectivities of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williarn~.~')
200-300pA. At 200pA the responsivity was stated to be well above 5000 v/w. Williams6' reported upon the properties of 74 photoconductive detectors arranged in four-element arrays as illustrated in Fig. 40.The dimensions of each of the long, narrow sensitive elements were 0.94 x 0.050mm2. Each array was evaluated initially in a test Dewar similar to that illustrated in Fig. 42, but without the silvered interior surfaces, and later in pairs (eightelement linear array) in a second test Dewar incorporating a cold shield and
40
0
180°UNOBSCURED FIELD-OF-VIEW 5 6 O FIELD-OF-VIEW 3.5 - 5 . 0 ~ BANDPASS FILTER
u)
C 30
z
3 LL
0
a
20
W
m
$
10
0 20
40
60
80
100 120 140 160 180 200 220 240
RESISTANCE ( K OHMS)
FIG. 57. Histogram of resistance values of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)
82
PAUL W . KRUSE
a 3.5-5.0~cold filter, as shown in Fig. 43. The effective background flux density in the former case was 1.4 x 1 0 I 6 photonscm-2 sec-', and was 2.0 x 1015photons cm-' sec- in the latter. The average spectral detectivity of the 74 unshielded, unfiltered 'detectors, and the improvement attendant upon cold shielding and filtering, is^contrasted to the room temperature background limited spectral detectivity in Fig. 54. Histograms illustrating the blackbody and spectral detectivities, resistances, and optimum bias currents, all'with and without cold shielding and filtering, are shown in Figs. 55-57'. Figure 55 shows the distribution in values of D*(500°K,840,1)before and after cold shielding and filtering. The improvement in detectivity with cold shielding and filtering is clearly evident in the shift in distribution toward higher values. Figure 56 illustrates the distribution in spectral detectivity, 0,*(4.6,840,1), with and without cold shielding and filtering. Here the improvement is marked ; no overlap exists between the two distributions. Figure 57 illustrates the resistance increase attendant upon cold shielding and filtering, indicating that the major portion of the carriers present in the unshielded detectors are produced by photoexcitation by the room temperature background radiation. The last histogram, Fig. 58, shows that the optimum bias current distribution is shifted toward lower values following cold shielding and filtering. As L e n n a ~ - ddid, ~ ~ Williams6' also categorizes the dependence of detectivity upon bias current, as illustrated in Fig. 59. Note that cold shielding and filtering has a moderate effect upon the distribution of detectors among the three shapes.
0
40
180°FIELD-OF-VIEW
v)
a
0
COLD 3 . 5 - 5 . 0 ~SPECTRAL EANDPASS FILTER AND 56" FI ELD -OF - V I E W
30
W
I-
W
n
lL
20
0
a W
g
10
3
z
0
10
20
30
40
50
60
70
00
90
BIAS CURRENT ( p A M P S ) FIG.58. Histogram of optimum bias currents of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)
2.
83
INDIUM ANTIMONIDE DETECTORS
SHAPE I
SHAPE 2
20
20
SHAPE 3
I
40 BIAS CURRENT ( p AMPS)
40
20
40 BIAS CURRENT (pAMPS)
BIAS CURRENT (pAMPS)
SHAPE I
74 DETECTORS VIEWING
I
SHAPE 2
1
SHAPE 3
UNOBSCURED 160' FIELD - O F - V I E W
56" F I E L D - O F - V I E W AND COLD SPECTRAL FILTER
FIG.59. Dependences of detectivity upon bias current for 74 77°K photoconductive detectors. (After Williams.60)
Finally, Table VI illustrates the uniformity within a single eight-element array incorporating a cold shield and filter. The range in detectivity values is k 18% ; that in resistance is k 15%. All detectors operate at the same bias current with similar dependences of detectivity upon bias. TABLE VI PROPERTIES OF AN EIGHT-ELEMENT PHOTOCONDUCTIVE ARRAYOPERATED AT 77°K WITH 560-FIELD-OF-VIEW COLDSHIELD A N D 3.5-5.0-p COLDFILTER' Cell number Characteristic 1
Bias current (pA) Resistance(ohms x Signal (pV) Noise (pV) D*(500,840,1) (cmHz"*/W x lo-'') DA*(4.6,840,1) (cmHz"'/W x lo-")
" After Williams.60
2
3
4
5
6
7
8
10 10 10 10 10 10 10 10 73 76 72 75 66 82 62 69 145 130 125 148 115 135 135 135 0.86 0.73 0.74 0.80 0.70 0.80 0.73 0.74 1.64 1.64 1.64 1.84 1.32 1.56 1.70 1.67 1.57
1.57
1.57
1.77
1.27
1.50
1.63
1.60
This Page Intentionally Left Blank
CHAPTER 3
Narrowband Self-Filtering Detectors M . B . Prince
. . . . . . . . . . . . . . 2 . Requirement of Direct Semiconductors . . . . . 3 . Tuning Techniques . . . . . . . . . . . 4. Binary III-V Materials . . . . . . . . . 5. Ternary 111-V Materials . . . . . . . . . 111. EXPERIMENTAL DATA. . . . . . . . . . . 6. Spectral Measurement Technique . . . . . . . 1. Binary Maierials-GaAs . . . . . . . . . 8. Ternary III-V Materials--lnAs,P, . . . . . . IV. SUMMARY . . . . . . . . . . . . . . I. JNTRODUCTION.
11. THEORETICAL DISCUSSION . . . . . . . . . 1. General Solution of Photovoltaic Detector Response
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
85 87 81 92 93 94 94 97 91 98 102 106
I. Introduction This chapter reviews a relatively new type of photovoltaic detector'.' that is of interest for infrared radiation detection. Such devices make use of the unusual absorption coefficient versus wavelength characteristics of a special group of III-V compounds and mixtures of compounds. When properly fabricated with these materials, p-n junction devices with a relatively narrow spectral response can be made. Narrow response does not depend upon a narrow-band filter (such as a multilayer thin-film filter) placed in front of the device, but depends rather upon the optical absorption of the material itself for filtering purposes. Thus these devices are called narrowband self-filtering detectors (NBSFD). In addition to improved reliability due to mechanical simplicity and a relaxing of the cooling requirements needed for use of external filters,narrowband self-filtering detectors have a very broad field of view and a spectral response which is relatively insensitive to the angle of incidence of the radiat ion being detected.
' A. Lopez and R. L. Anderson, Solid-State Electron. 7 , 695 (1964). D. B. Medved and S. Kaye, Bull. Amer. Phys. SOC. Series II,9,714 (1964).
86
M. B . PRINCE
Several of the applications' for solid-state detectors that require some restrictions on the wavelength span of their response functions are : (1) detection of fluorescence spectra from the nitrogen first positive band at 8911 A ; (2) detection of injection luminescent diode outputs from gallium arsenide devices ; and (3) detection of laser emission at 1.06 p. The design principles of the NBSFD are quite simple. Two requirements must be met :(1) a direct-gap semiconductor must be used, and (2) the device must be illuminated through a relatively thick base region, rather than through the thin diffused region as is the usual practice. Figure 1 illustrates the geometry requirements. The spectral response functions of p n junction devices are usually determined by the interaction of two distinct mechanisms. Free carriers are produced by the absorption of incident radiation at energies in excess of the band gap. These charge carriers may then be transported to the junction by diffusion or drift or by a combination thereof. Those pairs which reach the junction are separated by the field, and an external current or voltage is generated. Direct gap semiconductors usually have a rapidly varying absorption coefficient in the vicinity of the long wavelength cutoff. It can change by an order of magnitude in a wavelength interval spanning less than 100 A. If diffusion lengths for the minority carriers are much less than the thickness of the base region, only radiation within a very narrow band of energy will be absorbed close enough to the p-n junction for the resulting carriers to be collected. Part I1 provides a quantitative analysis of predicted spectral response functions for the geometries of the type shown in Fig. 1. Criteria for selection of specific material combinations are also formulated in this section. In Part I11 experimental results are described for two different materials
INCIDENT
RADIATION
X =W (JUNCTION PLANE)
X=d
LOIFFUSED REGION ( 5 0 - 7 5 8 ) FIG. 1. Geometry for narrowband detector.
3.
NARROWBAND SELF-FILTERING DETECTORS
87
demonstrating the general applicability of the concept : gallium arsenide for 8850 A, and indium-arsenide-phosphide solid solutions exhibiting narrow spectral response at 1.06 p. 11. Theoretical Discussion
I . GENERAL SOLUTION OF PHOTOVOLTAIC DETECTOR RESPONSE The theoretical spectral response characteristics are obtainable from solutions of the steady-state continuity equations with suitable boundary conditions. The steady-state equations for the minority carriers ( p , n ) in the regions of Fig. 1 for radiation impinging on the surface are p _ aN d 2 p_ _ -tax = 0,
+
dx2
L,
d2n dx2
Ln2
D,
n + -aN e-=x
__-__
=
D,,
0
The boundary conditions for these equations are
D,dp/dx = spp at x
=
0,
p(w) = n(w) = 0 at x = w ,
D, dnjdx
=
s,n
at x
=
d,
where the symbols are defined following Eq. (3). Since 1954 various paper^^-^ have been published relating to the spectral response of photovoltaic devices. These papers were primarily concerned with energy conversion with devices such as solar cells and nuclear batteries. One of the first of these papers was by Pfann and van Roosbroeck3. They have given an expression for the quantum efficiency [their Eq. (23)] which is relatively complex but does not take into account all the parameters for the device under consideration here. Wolf4 has derived equations for the contributions from both sides ofthe p-n junction to the quantum efficiency. In this chapter short-circuit conditions will be assumed in the operation of the narrowband self-filtering detectors. Thus Wolf's Eqs. (4) and ( 5 ) can be converted into the following equations for the contribution to quantum efficiency W. G. Pfann and W. van Roosbroeck, J . Appl. Phys. 25, 1422 (1954). M. Wolf, Proc. I.R.E. 48, 1246 (1960). D. A. Kleinman, Bell System Tech. J . 40,85 (1961). M. B. Prince and M. Wolf, J . Brit. IRE 18, 583 (1958).
88
M. B. PRINCE
from the two sides of the p-n junction :
Q, =
Q
=
2
e-aW
= aL,
+
+-spLp{exp[(l DP
- aL I?] LP
3
aLp+ 1
Qn+Qp.
where Q, is the quantum efficiency contribution from the base region, Q , is the quantum efficiency contribution from the diffused region, Q is the total quantum efficiency, J,, is the charge carrier flux in the base region, J , is the charge carrier flux in the diffused region, N is the photon flux, a is the absorption coefficient, L, is the hole diffusion length, L, is the electron diffusion length, s, is the front surface recombination velocity, s, is the rear surface recombination velocity, D, is the diffusion constant for holes, and D, is the diffusion constant for electrons.
In this discussion it is assumed that the geometry of Fig. 1 prevails with a bulk base region of n-type material and a rear diffused region of p-type material. This structure was chosen for the analysis because the experimental devices have this configuration. Since the diffused region has a concentration gradient of impurities, there is a drift field set up which should contribute to an improved quantum efficiency from this p-region. Kleinman5 has shown that the built-in field can be eliminated from the calculation by reducing the surface recombination velocity for the region of interest. This will be done in the calculations in this section. Equations (1) and (2) have been solved for
3.
NARROWBAND SELF-FILTERING DETECTORS
89
two special cases. These cases were chosen to be consistent with the experimental data using gallium arsenide devices. The values chosen are given below. Detectors have been fabricated by diffusion of zinc into n-type gallium arsenide. The base material employed for device fabrication had a range of carrier concentration from 2 x loi6 to 5 x 1017cm-3. The optical and electrical properties of n-type gallium arsenide have been extensively studied for doping concentrations in this range. It is possible to obtain acceptable values from the literature for all the parameters in the expression for quantum efficiencyfor gallium ar~enide.’-’~Of these, Hill,7 Braunstein et d.,’ Turner and Reese? and Kudman and Vieland” treat the optical properties of the n-type and p-type materials. Kudman and Seidel“ restrict the discussion to degenerate p-type gallium arsenide,and Sturge” and Hobden and SturgeI3 describe the semi-insulating variety. Figure 2 shows room temperature absorption spectra of n-type gallium arsenide as obtained from Hill’ and Braunstein et a/.* for the doping range of interest. Unless otherwise specified,the optical values in Hill’s work7 have been utilized. For N , E 2 x 10l6cm-3 the diffusion length (L,) should be of the order of 10-15 p. The surface recombination velocities were chosen for the n-type surface based on reported data14; for the p-type surface the infinite recombination velocity (due to the ohmic contact on the back of the device) was reduced to lo4 cm/sec in the light of Kleinman’s discussion. Equations (1)and (2) have been calculated as quantum efficiency (Q)versus absorption coefficient (ct) curves for two cases. Case 1 is the configuration of Fig. 1 with W = 50 p or 5 x l o v 3cm, and case 2 has W = 1OOp or cm. In both cases the other parameters are fixed : s p = i04cm/sec, = i0-3cm, = 10 cm2/sec, = 1W3cm, = 10 cm2/sec, and s, = - lo4 cm/sec.
L,, D, L, D,
In both cases the diffused region is 50 p thick.
’ D. E. Hill, Phys. Rev. 133, A866 (1964). R. Braunstein, J. 1. Pankove, and H. Nelson, Appl. Phys. Lerrers 3, 31 (1963). W. J. Turner and W. E. Reese, J . Appl. Phys. 35,350 (1964). l o 1. Kudman and L. Vieland, J . Phys. Chem. Solids 24,437 (1963). 1. Kudman and T. Seidel, J . Appl. Phys. 33, 771 (1962). ” M. D. Sturge, Phys. Rev. 125,768 (1962). l 3 M. V. Hobden and M. D. Sturge, Proc. Phys. Soc. (London) 78, 615 (1961). I 4 K. L. Ashley and J. R. Baird, IEEE Trans. Electron Devices 14, 429 (1967).
M. B . PRINCE
'I
1,000
-
-w+-z6
n = 5.3X 10 ~
0
0 LL
100-
0-DATA CALCULATED FROM NBSFD
0 0
z
0 + a
/i1 / I
I1I
/'j/l
0 m
m a
-_-_----' 10
/
I
/
/
n = 2.5 X d7
I '
1.30 9530
/
0
I
1.35 9175
I
1.40 eV0050
A-
1Y
A
FIG.2. Absorption coefficient for n-type GaAs (dashed curves after Braunstein et d.,* solid curves after Hill').
Case 1 curves for quantum efficiency versus absorption coefficient are given in Fig. 3. Curve A represents the contribution due to the front base region, curve B represents the contribution due to the diffused rear region, and curve C is the total response curve. From these curves two points should be noted: (1) Practically all the spectral response is due to those photons having a wavelength such that the absorption coefficient lies between 10 and 200Ocm-'; and (2) the front base region contributes more to the total response than the diffused region and its peak response is shifted toward higher values of alpha. (The quantum efficiency is defined as the number of electrons crossing the junction per photon incident into the device. These calculations do not take into consideration the surface reflectivity properties.) Figure 4 gives similar curves for Case 2 (which has the junction twice as deep as in Case 1). In this case several points should be observed: (1) The total peak response has been cut in half; (2) the pass band has been reduced to 10-500 cm- ; and (3) the peak response has shifted from an alpha value of 200 to 100 cm- These points will be considered later under the discussion of tuning techniques.
3.
I4
-
A CURVE = BASE REGIONB CURM:DIPFUSED REGION t CUR#= TOTAL RESPONSE
-
13 12 I1 -
-
10
91
NARROWBAND SELF-FILTERINC DETECTORS
-
-
-
ABSORPTION COEFFICIENT, a (cm-1)
FIG.3. Curves showing Case 1 response of base and diffused regions.
Solutions of Eqs. (1-3) under the extreme cases of letting (a) s, = sp + 0, and (b) s, = s p -+ 00 for Cases 1 and 2 yield curves that match those of Figs. 3 and 4 within & on the ordinates. This is as expected, since the diffusion lengths for these cases are small compared to the base region or diffused region thicknesses. 8
I
7 -
I
I
c/ ,/-/
6 -
/
\
.
I
CASE 2 CURVE A = BASE REGION CURVE B * DIFFUSED REGION CURVE C ' TOTAL RESPONSE
\
\
\
/
/ 57 5 -
/ /
\ A
\
ABSORPTION COEFFICIENT, a (ern-') FIG.4. Curves showing Case 2 response of base and diffused regions.
92
M. 8 . PRINCE
A simple approximation can be developed for the case where W % L, and surface recombination is neglected. The generation term g(x) for photon to electron-hole pairs is
g(x) = aN,e
-IIx,
(4)
where N o is the photon flux in photons/cm2 sec. In this case the variable g(x)is relatively constant over a diffusion length in the vicinity of the junction for values of wavelength where g(x) has a relatively large value at W. It becomes g = tlNoe-IIW. Under this approximation the particle current J is J
=
aNOLpe-uW,
(5)
and the quantum efficiency Q is
Q = J/N,
=
aLpe-uW.
(6)
The maximum value of the quantum efficiency is
Q,,,
=
(L,/W)e-
’.
(7)
The values of quantum efficiency in Eqs. (6) and (7) must be doubled to take into consideration both sides of the junction. 2. REQUIREMENT OF DIRECT SEMICONDUCTORS From the above general discussion it was noted that as the junction is moved further from the front surface both the total spectral response and the bandwidth are reduced. The bandwidth of interest is that for which M ranges from 10 to approximately lOOOcm-’. In order for this bandwidth to be narrow, the absorption coefficient should vary rapidly with wavelength (A) in this range. It so happens that this occurs with direct semiconductors. To show this, Fig. 5 presents a plot of c( versus 1 for a collection of several semiconductors. It is observed that the indium compounds and gallium arsenide have very steep slopes in the absorption-coefficient region of interest. These are all direct semiconductors, i.e., materials in which electrons and holes can recombine without the assistance of a phonon or by direct radiative recombination with the emission of a photon. It is not known whether or not all direct semiconductors have this steep slope (for example, the early data on GaSb as shown do not meet this requirement), but the recombination cross section should be relatively high in the narrow spectral region of the energy band gap compared to indirect semiconductors, in which recombination must be assisted with a phonon. In “indirect” semiconductors recombination takes place nonradiatively with the help of multiple recombination levels and the emission of many phonons into the crystal lattice.
3.
93
NARROWBAND SELF-FILTERING DETECTORS WAVELENGTH ( p )
310
62 124
413
207 I55 124 103 08 0775 248 177 138 113 0953 0826 0730
-
-
01 3 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9
10
I I
I 12
I 13
i
l
i
14
15
16
_ 17
ENERGY ( e V ) FIG 5 Absorption coefficient vs energy/wavelength
3. TUNINGTECHNIQUES
There are four methods by which the response characteristics ofthe NBSFD can be modified or tuned. The most obvious and the grossest technique is the selection of the material. From Fig. 5 it is observed that the wavelength of interest can be changed from approximately 0.9 ,u to approximately 4.0 p by changing from GaAs to InAs. Finer changes can be obtained by using ternary mixtures of 111-V materials. This technique for tuning is called compositional tuning. More will be given about this technique later in the chapter. A second technique, temperature tuning, allows for changing the spectral response by adjusting the operating temperature of the device. This technique can most readily be understood by using Fig. 6, a plot of the absorption coefficient versus wavelength for several temperatures for InAs.' At room temperature (298°K) the response will peak at about 3.7 p. By reducing the temperatuie to liquid nitrogen temperatures (77°K) the peak wavelength will shift to 3.0 p, and upon heating the device to 388°K the peak wavelength will shift to approximately 4.1 p. Similar shifts are expected for other materials. A third technique, which depends upon the depth of the junction below the surface impinged by radiation, has been described essentially in Section 1 of Part I1 where it was shown theoretically that as the junction depth is l5
H. Welker and H. Weiss, Solid
Stute Phys.
3, 56 (1956).
94
M . B. PRINCE
FIG.6. The behavior of the absorption constant of InAs at different temperatures.
increased the peak spectral response occurs at longer wavelengths. This technique is called junction depth tuning. Reverse biasing, the fourth tuning technique, depends upon the fact that when a p-n junction is reverse-biased by an external voltage supply the space-charge region is increased ; this increase occurs primarily in the more lightly doped side of the junction. In the case of the structure of Fig. 1 practically the entire increase takes place in the original base material and moves the effective junction closer to the radiation-impinged surface. Thus the effective junction depth can be changed after fabrication of the device, and the spectral response can be modified by changing the reverse bias. Specific data on these various methods of tuning will be presented in Part 111.
4. BINARY111-V MATERIALS As shown in Fig. 5, there are several binary 111-V materials that have the proper rapid change in absorption coefficient with wavelength for use in the NBSFD concept. These include most of the direct semiconductors (GaAs, InAs, InSb, etc.). The spectral response peak of an NBSFD is determined essentially by the energy gap of the material from which it is fabricated. For typical NBSFD geometries in gallium arsenide the peak occurs at photon energies approximately 0.05 eV greater than the band gap. 5. TERNARY 111-V MATERIALS
There are a number of specific wavelengths for which NBSFD’s would be useful, but for which there are no elemental or compound semiconductors
3.
NARROWBAND SELF-FILTERING DETECTORS
95
having the requisite energy gap. In these cases one must resort to solid solutions of various direct gap semiconductors. There is usually more than one solid solution of appropriate energy gap. In this subsection some criteria upon which a selection can be based are discussed. Of prime importance is the crystallographic structural quality that can be achieved in the solid solution. In considering various possible combinations of the III-V compounds, only those cases involving the mixing of two compounds which have one element in common will be considered, rather than the general quaternary systems, The liquid-solid equilibrium phase diagrams will not be discussed for two reasons: these have already been considered in the literature,16 and the work reported here involved growth of the solid solutions from the vapor phase only. There are eighteen systems among the nine III-V compounds formed with the elements Al, Ga, In, P, As, and Sb, considering only the ternary systems. In the early work on solid solutions between pairs of these compounds the conclusion was reached that the compounds were mutually soluble only over a very limited range.”*’* Later it was found that, in the cases of InAs-InP and GaAs-Gap, solid solution could be achieved through the whole composition range.’ 9*20 The suggestion was made2’ that solid solution could be achieved if the group V elements were mixed, but not if group I11 elements were mixed. Further studies, which have included eight of the quasibinary systems, indicate solid solubility through the entire range of composition ; however, in most cases single-phase material is obtained only after months of annealing if the solution is prepared from a melt.22~23 If the annealing is done on powder samples (as for X-ray powder photographs), single-phase material has been achieved by anneals over periods as short as two weeks. Homogeneous singlephase material is required for good p-n junction devices. A number of rules have been devised for predicting solubility in the case of binary substitutional alloys of simple metals, the most important being Hume-Rothery’s rules of atomic size and of electron-atom ratio. There is no rule which is generally applicable for combinations of the III-V compounds. Predictions have been made based on atomic sizes. The zincblende lattice (the lattice of interest) consists of two interpenetrating fcc lattices with groupJ. C. Woolley, “Compound Semiconductors” (R. K. Willardson and H. L. Goering, eds.), Vol. I, Chap. 1. Reinhold, New York, 1962. l 7 C. Shih and E. A. Peretti, J. Am. Chem. SOC. 75,608 (1953). W. Koster and B. Thoma, Z . Metallk. 46, 291 (1955). 0.G. Folberth, Z . Naturforsch. 10a, 502 (1955). 2o H. Weiss, Z . Naturforsch. ll a , 430 (1956). P. Baruch and M. Desse, Compt. Rend. 241,1040 (1955). 2 2 N. A. Goryunova and N. N. Fedorova, Zh. Tekhn. Fiz. 25, 1339 (1955). 2 3 J. C. Woolley and B. A. Smith, Proc. Phys. SOC.(London)72,214 (1958). l6
‘’
’*
96
M. B . PRINCE
I11 atoms on one and group-V atoms on the other. Since only those compounds having one element in common will be mixed, the mixing will take place in the form of substitution on one or the other of the fcc lattices, but not both. The effect of a difference in radius if a small atom such as A1 is substituted into the group-I11 fcc lattice on InAs will be to decrease the tetrahedral bond distance at the A1 sites, and it may be expected that there would also be an increase in the second-nearest-neighbor bond distance with distortion in the bond angles. This distortion can be minimized and the possibility of forming homogeneous single-phase solid solutions enhanced by choosing solutions in which the radii of the solvent and solute atoms are comparable. The effect of the radius ratios can be made more apparent by considering the actual nearest-neighbor distances in the compounds of interest.24These are simply the sum of neighboring radii. The difference in the nearestneighbor distances is of interest when two compounds with a common element are mixed, since this results in the lattice distortions at solute sites TABLE 1 THE18 POSSIBLE SYSTEMS OF THE MORE-COMMON 111 v COMPOUNDS, THE POSSIBLE WAVELENGTH RANGESFOR NBSFD’s. AND DIFFERENCE AETWEEN NEAREST-NEIGHBOR DISTANCES ANNIN THE TERMINAL COMPOUNDS
System In<Sb, P) In<Sb, As) In4As, P) Ga<Sb, P) GadSb, As) Ga - 1 ,
z 0.667[(q
+ 4)2+ 1.f1451~’~for
q
+ 4 < - 1.
The symbols not previously defined are as follows : mu* is the effective mass of holes in the valence band = 0.3 m, and B = 4n(2kR/h2)3’2(mu*)3/2 = 8.9537 x 10140K3/2cm- 3. In the range of x and T covered here the holes never become degenerate, so only the first approximation for the Fermi function was used. Starting with the above equations a computer program was written to set up various combinations of x and T, calculate p from Eq. (A2), calculate E, from Eq. (A4), and caIculate the reduced energy gap #. Then starting with an arbitrary q, calculating p from Eq. (A6), and integrating Eq. (A5) to within 0.5% a value of n - p was determined. A root finding program was next initiated which adjusted q and repeated the process until n - p m 0, or n = p = ni, the intrinsic carrier concentration. We have already given plots of n, versus x for various temperatures in Fig. 19, and of ni versus 1/T for various x values in Fig. 20. T.C . Harman and A. J. Strauss, J . Appl. Phys. 32,2265 (1961).
5. MERCURY-CADMIUMTELLURIDE AND CLOSELY RELATED ALLOYS
255
This entire calculation is for intrinsic material, and therefore only degeneracy due to intrinsic carriers is included; however, an estimate of the doping level allowed before these intrinsic results are invalidated can be made by assuming that doping levels as high as the intrinsic carrier concentration are allowed and determining these levels from Fig. 19 and 20.
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Thermal Detectors
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CHAPTER 6
The Pyroelectric Detector E. H . Putley
I. THEPYROELECTRIC EFFECT, .
.
.
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 3 . Principal Noise Sources . 4. Total Energy Detector .
. .
. .
.
. . . . . . . . . . . DETECTOR . . . . . . . .
11. THEPYROELECTRIC DETECTOR . .
I , The Thermal Circuit . 2. The Electrical Circuit. 111.
CONSTRUCTION OF PYROELECTRIC
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
5 . Choice of Material . . . . . . . . . . . . . . 6. Details of Construction . . . . . . . . . . . . . 7. Performance of RRE Pyroelectric Detector. . . . . . . . 8 . Comparison with Other Detectors . . . . . . . . . . APPENDIX . . . . . . . . . . . . . . . . . NOTEADDEDI N PKOOF. . . . . . . . . . . . . .
259 26 1 26 I 263 266 272 213 273 275 276 279 283 284
I. The Pyroelectric Effect Crystals of noncentrosymmetrical structure make up 21 of the 32 types of symmetry. Of the 21 noncentrosymmetric classes, ten (which are all piezoelectric) can exhibit spontaneous electric polarization. However, an external electric field will not normally be observed, since if the material is a conductor, its mobile charge carriers will assume a distribution which neutralizes the internal moment, while if it is an insulator, stray charges will be attracted to and trapped on the surfaces until the surface charge associated with the polarization is neutralized. The charge distribution produced in this way near the surface of an insulator is relatively stable, unable to respond quickly to sudden changes of the internal dipole moment. Thus, in particular, if the temperature of the material is changed, the dipole moment may also change, and this change will produce an observable external electric field. Thus, although the dipole moment is not directly observable, its temperature coefficient is. This temperature coefficient is called the pyroelectric coefficient (Cady’). The purpose of this chapter is to discuss the exploitation of this effect as a means of detecting infrared radiation.
’ W. G. Cady, “Piezoelectricity.” McCraw-Hill. New York, 1946. 259
260
E. H. PUTLEY TABLE 1 THEPROPERTIES OF SOMEPYROELECTRIC MATERIALS AT 300°K
Material ~~
Tourmaline
4
x
BaTiO,
Triglycine sulphate (2-3.5) (TGS) (NH,CH2COOH),.H,SO4 Li,SO,,H,O
x
'O
lo
*
lo-'
1.0 x 10.8
,o
LiNbO, LiTaO, SbSI NaN02
10
~
6 x 2.6 10-7
1.2
x
lo-'
I 60 (11 polar axis) 4100 (Ipolar axis) 25-50 10
OS
0.97 -0.4
30 (11 polar axis) 104
x lo-'
6.0
x
10''
1.69
17 x
lo-'
2.05
6.8
4.64
75 (Ipolar axis) 56 8.0
9
0.29 0.96
8.2 2.1
Table I gives the magnitude of the pyroelectric coefficient (expressed in C c m - Z o K - ') for some typical materials. When it is recalled that a sensitive C it is seen that use of electrometer can detect a charge of about 5 x the pyroelectric effect should enable change in temperature of less than 1pdeg to be detected, and in fact it has been used for this Any sensitive thermometric element can, in principle, be used as a thermal infrared detector. This application of the pyroelectric effect was suggested by Yeou Ta4 and Chynoweth,s and a detailed analysis of the characteristics of the pyroelectric detector was first made by Cooper showed that it should be possible to produce a pyroelectric detector of performance close to the limit set by the surroundings at room temperature. Unfortunately, Cooper was not able to achieve this performance in practice, apparently due to the limitations of the pyroelectric materials then available, Since that time improved materials have been developed. Several laboratories have been studying the development of improved pyroelectric It appears S. B. Lang and F. Steckel, Rev. Sci. Znstr. 36,1817-1821 (1965). S. B. Lang, Natl. Bur. Std. (U.S.),Tech. News Bull. 51, 193 (1967). Yeou Ta, Cornpt. Rend. 207, 1042-1044 (1938). ' A. G . Chynoweth, J . Appl. Phys. 27,78-84 (1956). J. Cooper, Rev. Sci. Instr. 33, 92-95 (1962). ' J. Cooper, J . Sci. Instr. 39,467-472 (1962). * A. L. Stanford, Jr., Solid-state Electron. 8, 747-755 (1965). G. A. Burdick and R. T. Arnold, J. Appl. Phys. 37,3223-3226 (1966). H. P. Beerman, Am. Ceram. SOC.Bull. 46, 737-740(1967). ' I A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, and B. Wyncke, J . Phys. 26,345-360 (1965). L. S. Kremenchugskii, A. F. Mal'nev, and V. V. Samoilov, Prihory i Tekhn. Eksperim. No. 6, 169-171 (1966) [Instr. and Experim. Techniques (English Trans/.)No. 6, 1460 (1966)l. l 3 K. Takdmi, K. Suda, and M. Koga, Oyo Butsuri 37, 147-156 (1968). l4 J . H. Ludlow, W. H. Mitchell, E. H. Putley, and N. Shaw, J. Sci. Instr. 44, 694-696 (1967); J. H. Ludlow, W. H. Mitchell, and E. H. Putley (to be published).
'
6 . THE PYROELECTRIC DETECTOR
261
now that the performances being achieved are beginning to approach the ideal limit. In addition, it has been possible to demonstrate that under certain conditions a useful fast pyroelectricdetector (with an effective response time of less than 1 psec) can be produced.
II. The Pyroelectric Detector When the pyroelectric detector absorbs radiation its temperature rises, changing its surface charge. To calculate its performance, both the thermal and electrical characteristics must be considered in detail and the sources contributing to the detector's noise must be enumerated. These aspects are discussed in detail in the following three sections. In this way the performance of the pyroelectric detector can be calculated. There are three ways in which a pyroelectric detector may be used : (1) To detect a signal modulated at a constant angular frequency w ;(2) by combining a detector operating in this mode with a frequency-equalizing amplifier, a receiver with a very short (less than 1 psec) response time suitable for observing transient signals, such as laser pulses, may be produced ; and (3) the pyroelectric element can be used to store the total charge liberated by a transient signal, Measurement of this charge determines the total energy of the transient. The discussion of the next three sections is concerned primarily with detectors employingthe first two modes of operation, but in the following section the charge storage mode is also discussed. 1 . THETHERMAL CIRCUIT Consider a thin plate of pyroelectric material held in position by supports of low thermal conductance in an evacuated constant temperature enclosure of temperature T"K. Then the thermal conductance coupling the plate to its surroundings will be mainly determined by radiative exchanges. From Stefan's law, if the plate is at a temperature T + 8, the heat flow from the plate to its surroundings is GRe,where GRis the radiative conductance, which for a unit area is GR = 490T3, (1) where q is the emissivity of the surface and (T is Stefan's constant. If the area of the plate is A and both sides radiate with the same emissivity, then GR = 8 v g A T 3 . (2) Since in most cases there will be other significant contributions to the thermal conductivity, GR is the limiting value to which the actual conductance G tends in ideal circumstances. Although this will not apply to all processes M. F. Kimmitt, J. H. Ludlow, and E. H. Putley. Proc. IEEE 56, 1250 (1968).
262
E. H.PUTLEY
contributing to the conductance, we will assume G is proportional to A (i,e., G = gA). If the thickness of the plate is d cm and its specific heat is c J gm-' deg- and its density S gm cmP3, the plate's thermal capacity is
'
H = dAd, (3) where c' = cS is the volume specific heat. If the plate is exposed to a beam of radiation containing a component modulated at angular frequency w, the incident power of the beam can be written
f
=
f,
+
(4)
loejWf,
where 1, > I,. The temperature of the plate is found by solving the equation ?I = H(dB/dt)
+ GB.
(5)
Solving for the amplitude of the component tlo at angular frequency w of the excess temperature gives
+ o2H2)-
ti',
= r71(o(G2
lj2,
(6)
and q5 = tan-'(oH/G) is the phase difference between the radiation and temperature oscillations. Having calculated O w , the corresponding pyroelectric charge appearing on the surface of the element can be obtained at once and the output voltage produced calculated by considering the electrical circuit of the element. Before doing this the thermal circuit will be considered in more detail. The simple calculation just outlined for a,, assumes that the incident radiation is absorbed uniformly throughout the sample. If the material has a large absorption coefficient a cm ' or if its surface is coated with a thin absorbing layer, this assumption may not be justified. In some regions of the infrared spectrum the absorption coefficients of pyroelectric material appear to be greater than 1000 cm-', so that the radiation will be absorbed in a distance less than 10 p , which is likely to be less than the thickness of the plate. Hence the thermal behavior when the absorption is nonuniform must be considered in more detail. An exact calculation is difficult, but a useful insight to the problem is obtained by considering the case where the radiation is absorbed at the surface of a semiinfinite slab, If we consider again the component of excess temperature at the angular frequency w, we find that a damped temperature wave is propagated into the material. The behavior can be calculated by considering the distributed thermal circuit for the plate. An element of thickness dx will have a thermal capacity c'A d x and a thermal resistance d x / K A, where K is the thermal conductivity. This distributed circuit can be treated in exactly the same way as an electrical circuit. Then it is found that the bulk material presents to the absorbing layer a thermal ~
6. THE PYROELECTRIC DETECTOR
263
+ ~)(&oKc’)”~A:
(7)
admittance Y = (1
while the propagation constant for the thermal wave is
y = (I
+j)(~c’/2K)’~~.
Hence if the excess temperature at the surface is written 80 = 8, cos ot ,
(8) (9)
the excess temperature at a distance x below the surface will be
6,
=
6, exp[( - ~ c ’ / 2 K ) ’ / ~cos[ot x]
-
(o~’/2K)’/~x].
(10)
Thus at a depth below the surface
d T = (2K/oc’)1’2
(11)
the amplitude will be reduced to l/e of its value at the surface, while at the ’ ’ ~wave will be in quadrature with the slightly greater depth ~ ( K / ~ w c ’ )the wave at the surface. Hence if the incident radiation is absorbed in a very thin surface layer, the lumped circuit approximation will only be valid if the thickness of the pyroelectric plate is less than 6,. If 6 , is small compared with the thickness of the plate, then the thermal admittance of the thick slab must be included in the thermal circuit. To indicate the magnitudes involved, typical values for c’ and K are 1.5 J c m - j O K - ’ and 5 x l o d 3W cm-’ O K - ’ , respectively, giving 6 , = 3.3 x 10-2f-”2cm, where f is the frequency in hertz Thus for f = 100 Hz, BT = 33 p, while f = 10 kHz gives 6 , = 3.3 p. Hence 6, could become small compared with the thickness of the plate at relatively low frequencies, so that if the absorption coefficient is high, or the surface is blacked, the distributed thermal circuit must be used to calculate the thermal characteristics of the pyroelectric element. 2. THEELECTRICAL CIRCUIT If the pyroelectric coefficient is p and the area of the electrodes A (which for the present will be assumed to be the same as the receiving area; an alternative configuration is discussed in the appendix), the alternating temperature component 8, will produce an alternating charge pA8,. If we represent the element as a capacity C, in parallel with a resistance R,, the alternating charge on the electrodes is equivalent to a current generator i, = o p A 8 , in parallel with the capacity. If the element is connected across the input of an amplifier whose input impedance can also be represented by a capacity and a parallel resistance, the voltage applied to the amplifier is found by calculating the voltage across the equivalent circuit for the combined impedances (see Fig. 1).
264
E. H. PUTLEY
Detector
Arnplif ier inpul
Equivalent circuit
FIG. 1. Equivalent electrical circuit of detector and amplifier input.
Thus I/ =
i,[Zl
=
i,R( 1
+
WZZEZ)
-
,
where zE = RC. Hence V = WpAB,R(l
+ w2rE2)-112.
Substituting for 6 , from Eq. (6) gives 9v
=
V/ZU = q(wpAR/G)(l
+ C U ~ T E ~ ) -+~ w~ ~TT( )~ 2
2 -1/2
,
(13)
where rT = H/G is the thermal time constant. (This result will still apply if the distributed thermal circuit has to be used, provided the correct values are used for H and G.) Bv is the voltage responsivity (output voltage/input radiant power) of the pyroelectric detector.
w
FIG.2. The log-log plots of 0, and W, against w.
265
6. THE PYROELECTRIC DETECTOR
Figure 2 shows the frequency dependence of 8, and Bv.The former is constant at low frequencies, but varies as f - when f % (2mT)- ; the latter is zero when f = 0, is proportional to f when f < (27tTT)- ', (27~7,)- ', and varies asf-' whenf ( 2 7 t t T ) - ' , (27q4-l. Depending on the parameters of particular materials, zTmay be greater or smaller than zE.In the intermediate
'
Frequency (HA
FIG.3. Performance of a TGS detector with an XE 5886 amplifier. The resistance and capacity are measured values. Measured values for the responsivity are plotted, but the curve is calculated from Eq. (13) using the following values for the parameters : = 0.23, p = 2 x lo-* C cm-ZPK, G = 4.3 x JPK, 77. = 150 msec. The noise voltages Ah, AVT, and AVRare calculated from the electrical and thermal parameters of the detector, while AVA and AV, are measured. These noise sources are used with the responsivity to obtain the calculated curve for the NEP which is compared with the directly measured experimental curve.
266
E. H. PUTLEY
frequency region (27n,,J1 < f < (27c~,,,~~)-',W v is independent off: These remarks assume that the quantities p , H , G, C, and R are all independent of frequency. In actual materials some of them will usually show some frequency dependence (see, for example, the results plotted in Fig. 3), but this has not been found to be large enough to alter significantly the behavior of the responsivity from that given by Eq. (13). The order of magnitudes of zEand oT for the type of device we have measured fall within the range 1 0 4 . 1 sec. Since for the majority of applications the frequencies of interest are at least 10 Hz and in some cases are greater than 1MHz, the high frequency approximations of equations (6) and (13) are sufficient most of the time, i.e.,
0,
=
qIJuH,
(14)
qpA/wHC. Expressing (15) in terms of the material parameters, Wv
(15)
=
WV = ( l / ~ E ' ) ( ? P / ~ c ' ) ( ~ / A ) , (16) where E is the dielectric constant and E' the permittivity of free space. Substituting the numerical values given in Table I1 gives
.*"= 2.4 x
103(~~)-1
for A = 10-'cm2
= 2.4 x losf-' = 2400
vjw for f = 100 Hz.
V/W TABLE I1
PROPERTIES OF
THE
PYROELECTRIC MATERIAL ASSUMEDFOR 6
THE
CONSTRUCTION OF FIG. ~
Pyroelcctric coefficient p Resistivity p Dielectric constant c Volume specific heat c' Thermal conductivity K Emissivity q Absorption coefficient c1
~~~
~
2 x 10-*Ccrn-*OK-' 10'* ohm cm 10 1.5 J c m - 3 OK-' 5 x lo-' W cm-' OK-' 1 103 c m - l
3. PRINCIPAL NOISESOURCES The equivalent circuit (Fig. 4) shows the principal noise sources. These are (1) temperature or radiation noise, (2) Johnson noise in equivalent shunt resistance, (3) amplifier current noise, and (4) amplifier voltage noise.
6. THE PYROELECTRIC DETECTOR
AVT AVj
267
AV, AVA
FIG.4. Equivalent noise sources for (a) primary sources, and (b)equivalent voltage generators at amplifier input.
These will be considered in turn and then combined to determine the noise equivalent power or detectivity.
a. Temperature or Radiation Noise If a small body of thermal capacity H is coupled to a large heat sink at temperature T via a thermal conductance G, it will attain the same temperature T, and when thermal equilibrium is established the mean power flow between the body and the sink through the conductance G will be zero. However, it will have a fluctuation spectrum with an rms value16 AWT
=
(4kT2G)”’.
(17)
It is also possible to consider the blackbody radiation incident when the element is placed inside a blackbody enclosure at temperature T. The fluctuation in the radiation power absorbed and emitted can be calculated using radiation statistics. Ifthe element absorbs uniformly throughout the spectrum, the result obtained is similar to Eq. (17) but with G replaced by GR, the radiative conductance given by Eq. (2). Since GRis the minimum value G has when the element is coupled to its surroundings only by radiative exchanges, the radiative fluctuation is the limiting value to which Eq. (17) tends. In an ideal detector only the radiation term would contribute to the noise. I6
R. Clark Jones, Aduan. Electron. 5, 1-96 (1953).
268
E. H. PUTLEY
The temperature noise voltage produced by AWT is calculated by treating A W, the same way as an incoming signal. Hence
A VT
= 9v(A
;
(1st
7 appears in Eq. (18) because gvis defined in terms of the incident power
while Eq. (17) is given in terms of the power absorbed.
b. Johnson Noise There will be a Johnson noise voltage associated with the equivalent circuit resistance R (Fig. 1) given by
Ah = (4kTR)”’
(19)
(for a 1 Hz bandwidth). Referred to the amplifier input (Fig. 4) the corresponding voltage is AVJ = (4kTR)”’(l
+ W’T~’)-’’’.
(20)
At high frequencies this becomes AV,
=
(~~T)”’/UCR’”,
which shows that at high frequencies
(21)
A 5 is reduced by making R large.
c . Amplifier Noise
The noise characteristics of both vacuum tubes and solid-state devices can be represented by the combination of a voltage generator AVA in series with the input and a current generator AiA in parallel. Both these generators may be frequency dependent. Figure 5 shows typical values for some types of amplifier suitable for use with pyroelectric detectors. The voltage generator represents noise sources which are independent of the circuit connected to the input of the amplifier, while the current generator represents sources such as grid current noise whose relative importance depends on the circuit impedance. Thus AV’ appears in Fig. 4, while AiA is replaced by the equivalent voltage generator A y, where AK
=
R &A (1
+ W2~E2)p1/2,
(22)
which at high frequencies becomes
AK = Ai,/wC.
(23)
d . Comparison of Noise Sources-Noise Equivalent Power The four noise generators shown in Fig. 4 can be replaced by an equivalent generator AVN formed by summing the squares : (AV#
= (AV,)’
+ (AK)’ + (A&)2 + (AV,)’.
(24)
269
6. THE PYROELECTRIC DETECTOR
XE 5886 triode connected
1
-----A XE 5886 pentode connected
XE 5886 pentode connected
I
102
I
I0 3 Frequency
I
I0 4
-
J
Io5
(Hz)
FIG.5. Noise characteristics of amplifiers. The frequency dependence of the equivalent current and voltage generators is shown for the X E 5886 miniature electrometer triode and pentode connected and for the BFW 11 FET.
Suppose an incident signal of rms power PNproduces an rms signal voltage V, equal to AVw Then
PN = KJ%v
= AVN/Bv
(25)
is the noise equivalent power (NEP) or signal power required to produce an output voltage equal to the noise voltage. If in addition to knowing the pyroelectric material parameters the four noise generators in Eq. (24) are known or can be measured, the noise equivalent power of the detector can be measured. As defined by Eqs. (18), (21), (23), and (24), the NEP refers to unit amplifier bandwidth. If the bandwidth is B, the NEP will be increased
270
E. H. PUTLEY
by the factor B1/2. It is sometimes convenient to use instead of the NEP the detectivit y
D
=Pi1.
(26)
Often the performance of a detector is expressed in terms of the normalized detectivity D”,
(27) since in many cases AT/, varies as A’/’. However, as the following discussion will show this relationship only applies to pyroelectric detectors if AVT or AV, is the dominant noise source. In many instances either AK or AV’ is found to be the principal source of noise, so that the use of D* to discuss pyroelectric detectors can be misleading. To discuss the relative importance of the four noise sources combined in Eq. (24) and to show how they depend upon the properties of the pyroelectric materials, expressions for the NEP will be written down in which each noise source in turn will be assumed to be so large that the others can be neglected. High frequency operation will be assumed and the results will be expressed in terms of the bulk properties and the detector dimensions. This will show that the relative importance of the different noise sources depends in a different way on both material parameters and dimensions. This makes it difficult, therefore, to write down a single figure of merit for the comparison of pyroelectric materials. However, by making numerical estimates of the quantities involved (as shown in Fig. 3, for example) it is easy to see which parameters are the most important for any particular case. By using equations such as (15), (16), (IX), (21), (23), and (25) the following expressions for the NEP are obtained in the high frequency approximation :
D* = DA’lZ,
PN,(cmp = AV,/.%’v = (l/ll)(4kT’)’’Z(g)1i2A f“,johnson
(28)
= A Y / ~ & V = ( I / ~ ) ( 4 k T ) ” 2 ( ” / ~ ~ ” 2 ) ( A d ) ” 2 , (29)
AK/WV
( l / ~Ai) ( c ’ / ~ ),d
P N , amp current
=
f“,ampvoktage
= A L ‘ C ~ V= ( l / q ) (AVA)(C’E’~:/JI)A. ~
(30) (31)
Figure 6 shows some numerical examples calculated using typical values for a pyroelectric material (see Table 11) similar to lithium sulphate. This shows that for large area detectors and for high enough frequencies, the amplifier voltage noise will be the most important, but for smaller areas and low frequencies the behavior is more complicated. It should be possible to choose an amplifier with sufficiently small current noise to reduce this noise below Johnson and radiation (temperature) noise. Johnson noise can only fall below radiation noise with the parameters chosen if the thickness of the
271
6. THE PYROELECTRIC DETECTOR
16'
10-1
I
10
A (crn2)
FIG.6. Noise equivalent power as a function of area as calculated from Eqs. (28H31)using data from Table 11. These calculations assume that a thickness of the detector of l o p is the thinnest practicable for an unsupported element. The results indicate that the amplifier contributes the main sources of noise determining the NEP. This conclusion seems at first sight inconsistent with the experimental results shown in Fig. 3. However, the resistance of the detector measured for Fig. 3 was lower than has been assumed for this figure; hence the Johnson noise is greater in Fig. 3. To achieve the results predicted in this figure requires material of higher resistivity than was used for the detector of Fig. 3.
element can be reduced below 1 p. Since it is likely to be very difficult to produce elements less than 10 p thick without supporting them on a substrate which would increase the temperature noise excessively, it appears that radiation-noise-limited performance will only be obtained by the discovery of pyroelectric material with superior parameters to those given in Table 11. Nevertheless, taking the minimum practical thickness as about 10 y there
272
E. H. PUTLEY
is a good chance of making a detector that approaches within an order of the ideal limit. Its NEP would then compare quite favorably with that of other room temperature thermal detectors, and as the calculations given in Fig. 6 show, this performance should be attainable with the pyroelectric detector at frequencies well in excess of l/z, Thus the frequency response attainable should be very superior to that obtained with other thermal detectors, and in fact be comparable to that obtained with the slower types of photoconductor. 4. TOTALENERGYDETECTOR Consider a pulse of radiation absorbed near the surface of a relatively thick plate of pyroelectric material attached by its rear surface to a heat sink. The temperature of the surface will rise at once and a temperature wave will propagate into the body of the pyroelectric element. If the duration of the pulse is short compared with the time taken for the temperature rise to reach the rear surface of the element, then the only way energy can leave the element before the pulse is completed is by radiation from the front surface. Comparison of the radiative conductance with the thermal conductance of the slab (cf. Section 1) shows that the radiation loss will be negligible. Hence the pyroelectric charge produced will be proportional to the energy of the pulse. It can also be shown that the total charge is independent of the spatial distribution of the incident energy across the receiving area of the element.’ If the element has an electrical (RC) time constant which is long compared with the duration of the pulse, then the charge leakage will also be negligible. Hence measuring the charge produced using a suitable electrometer circuit will give the total energy of the pulse, independent of the duration of the pulse and of its exact spatial distribution. Study of the thermal circuit shows that if an abrupt increase in temperature occurs at the surface, the time required for the temperature at a distance 1 from the surface to rise to l/e of the surface value is
12c’/K.
(32) Hence if z is the duration of the pulse, the thickness d of the plate must satisfy the condition d 9 (KZ/C’)’/~ if no energy is to be lost during the duration of the pulse. If t x lmsec, then I z low2cm, and thus a relatively thick plate is required to satisfy this condition. Assuming that this condition is satisfied, the output voltage is given by z=
v(t)= (Ap/c’4 (1/C)
sd
d x ) exp[(x
- t ) / t E l dx
9
(33)
where q(t) is the energy flux per unit area absorbed by the detector. This expression simplifies if the electrical time constant is either long or short
6. THE PYROELECTRIC DETECTOR
273
compared with the duration of the incident signal. In the first case the integral is zero except when x x t, so that V ( t )= (Ap/c’d)Rq(t).
(34)
In the second case the exponential term approximates to unity over the range of integration, so that
Thus operation with a long electrical time constant gives a signal output proportional to the total energy of the pulse. Since pyroelectric materials with values of T~ 9 1 msec are commonly used, this condition is easily satisfied. If the time constant is reduced by shunting with a low value resistor, then the signal output will follow the shape of the pulse. Resolving times as short as 1 p e c have been obtained in this way. The total energy mode of operation has been used for measuring the energy of pulses in shock tube^,^.'^ hypersonic wind tunnels,18 and of laser pulse^.'^^^^ Attempts to use the fast mode have been of limited success due to the occurrence of elastic resonances. For this application the detector using frequency equali~ation’~ seems to be more suitable (see Section 7). The difference between the performance of these two detectors is probably due to differences in construction (the frequency-equalizeddetector is made very thin and is not supported at its back) which suppress the 100kHz resonances found when total energy detectors are used with short electrical time constants. 111. Construction of Pyroelectric Detector 5 . CHOICE OF MATERIAL
Examination of Eqs. (28)-(31) shows that suitable material will have a large pyroelectric coefficient, a high resistivity, a small dielectric constant, and a low thermal capacity. In addition, 9 must be made as close to unity as possible, either by using material with a high absorption coefficient or by depositing a suitably chosen absorbing layer on the front surface. The thermal conductance g must be made as small as possible, by careful design of the detector mounting. It is not possible to formulate these requirements by a single combination of the parameters as a figure of merit, since, as the equations for the NEP show, the precise combination for optimum performance ”
l9
A. D. Wood and J. C. Andrews, IEEE Trans. Aerospace Electron. Systems 3,356-367 (1967). C . R. Spitzer. I E E E Trans. Aerospace Electron. Systems 3,349-355 (1967). M. Shimazu, Y.Suzaki, M. Takatsuji, and K. Takami, Japan. J . Appl. Phys. 6, 120 (1967). R. W. Astheimer and R. E. Buckley, Rev. Sci. Instr. 38, 1764-1768 (1967).
274
E. H. PUTLEY
depends upon which noise source is dominant. Thus if we were to focus attention on Eq. (28) only, we might conclude that we need only worry about the design of the thermal circuit to achieve background-radiation-limited performance, which is clearly not the case. The choice of the best parameters for minimizing amplifier noise will depend on the relative values of AVA and A& for a particular amplifier, and this will depend upon the operating frequency. Thus the optimum choice of material and design of detector can only be made by considering each of the four equations for NEP in turn. The values obtained for the NEP also depend on the dimensions. The area A will be determined by the particular requirement. Since PN,temp and PN,Johnson vary as A l”, PN.amp current is independent of A, and PN,ampvoltage is proportional to A, the choice of A will affect the relative importance of these noise sources. Both PN,Johnson and PN,ampcurren, are improved by making the thickness d small. If this is made too small, it will reduce the absorption of the element and will introduce fabrication problems. In addition to these factors, other considerations include the ease of preparation of the material, its long term stability, and its piezoelectric and elastic properties which determine the extent to which microphony is a serious problem and the limitation by mechanical resonances of the high frequency performance. The relevant properties, as far as they are known, of likely materials are summarized in Table I. Although this table shows that promising materials include TGS, Li,S0,.H20, LiNbO,, LiTaO,, NaNO,, and SbSI, most of the recent work on pyroelectric detectors has been based on TGS. The following remarks on detector construction and performance apply primarily to a TGS detector, although most of them would apply to the other materials as well. The optical properties of these materials have certain features in common. Single crystals are transparent in the visible range, but become strongly absorbing at a wavelength of a few microns. Near 10p the absorption is high and remains so until the submillimeter region is reached, where it starts to fall again, Figure 7 shows typical transmission data for TGS. Although the absorption is high near the l o p wavelength, there is finite transmission in samples of thickness 2 0 p or less. Since for other reasons it is very desirable to use thin specimens, careful design of the front surface electrode is required to optimize the absorption. This becomes more important for detectors intended for use at submillimeter wavelengths. In the detectors so far used for submillimeter work this has not been done, so that further improvement in performance can be expected. Similarly, if pyroelectric detectors were required to have optimum performance in the visible or near-infrared, using the front surface layer as a black would enhance the performance.
6. THE PYROELECTRIC DETECTOR
-8
50
-
275
,--.,
7
~
zg 3 0 -
/'
\
/'
c 40-
0
/
//
,/
e t-
/I
20 /
10 -
I
i
/
I
I
,I /
OI
10
I
I00
I000
FIG. 7. Transmission of TGS plate 15 p thick. (The results for A < 15 p were obtained by Mullard (Southampton),20aand the results for I > 33 p are based on an extrapolation of measurements by Dr. G. Chantry,zobN.P.L.)
6. DETAILS OF CONSTRUCTION
Single crystals of TGS are grown by the controlled cooling of an aqueous solution. These crystals exhibit a well-defined cleavage plane normal to the pyroelectric axis. Hence location of this cleavage plane provides a simple method for determining the direction of this axis. Once this has been established, correctly oriented plates about 1 mm thick can be cut from the crystals using a wire saw. Elements of thickness between 10 and 20 pare then prepared from the plates by grinding with BAO abrasive in lapping oil and finally polishing using 0.3 p Linde powder in glycerine. Electrodes are evaporated onto the plates, using a thick deposit of gold for the rear electrode and a semitransparent nichrome electrode (500 ohms per square) on the front surface. The electroded element is then cemented around its edges to a metal plate which forms the heat sink and defines the aperture of the detector. A connecting wire is then attached to one face of the detector using a small blob of cold setting silver paste, while contact to the second face is made via the metal plate and conducting cement. This detector subassembly is then mounted in a case which contains at least the first high input impedance stage of the amplifier, but it is often convenient to include a following integrated circuit amplifier here. The case may be fitted with a rigid window and hermetically sealed or evacuated. Where the highest sensitivity is not required the sealing of the case is not essential. Mullard (Southampton), unpublished data 'ObG. Chantry, unpublished data.
276
E. H. PUTLEY
Reor electrode Heat sink
Solid state amplifier
1
Mylar window
/ Semitransparent front electrode
Pyroelectric
u
1 cm
FIG. 8. Schematic diagram of RRE detector. (After Ludlow et
af.14)
Figure 8 illustrates the type of detector constructed at the Royal Radar Establishment (RRE), while Fig. 9 is the circuit diagram of the amplifier included in the detector unit.
7. PERFORMANCE OF RRE PYROELECTRIC DETECTOR a. Noise Equivalent Power
Figure 3 shows the performance obtained with a pyroelectric detector constructed as described. The figure shows measured values for the responsivity, NEP (using a 500°K blackbody), and the impedance of the detector. These are compared with the responsivity calculated from Eq. (13) and with f
12v
1 FIG.9. Circuit diagram of amplifier (including frequency equalization section) used with R R E detector.
6 . THE PYROELECTRIC DETECTOR
277
calculated values for the NEP obtained by calculating the noise voltages [Eqs. (18), (21), and (23)] and using these in Eq. (24) to calculate the NEP. The calculated values for the various noise voltages are also shown. The impedance was measured using a Wayne Ken- type B221 transformer bridge with external source and detector. The reactive component was found to consist of a capacity (45pF) independent of frequency. The parallel resistive component is plotted in Fig. 3. The thermal characteristics were determined by measuring transient response at very low frequencies (- 1 Hz). All the parameters required to calculate the responsivity were known independently except q. The value of q was chosen (q = 0.23) to fit the experimental points. Since no special steps have been taken to ensure maximum absorption of radiation, the value assigned to q is not an unreasonable one, while at the same time indicating the possibility of a fourfold improvement in performance with more careful design of the front electrode. Considering the noise sources, it appears that Johnson noise A 6 is the dominant one below lOkHz, although the amplifier voltage noise AVA becomes greater above 10 kHz. The amplifier used was an XE 5886 miniature electrometer triode, which gave a slightly better performance than the best available solid-state device (the BFW 11 FET). The next most important source of noise was the temperature-fluctuation noise, while the amplifier current noise A F was smaller still, about the same value as the radiation noise AVRfor an ideal detector of the same area. Having calculated these noise generators using Eqs. (18), (21), or (23) with the data in Fig. 3, the NEP was calculated using Eq. (24). The calculated and measured NEP’s are compared in Fig. 3. At low frequencies the agreement is good, but above 100Hz the measured NEP is superior to the calculated one. Since the Johnson noise is the main noise source, this could imply an error in the measurement of resistance, since if the measured resistance were too small, the calculated Johnson noise voltage would be too large. Since the impedance of the TGS element is somewhat dependent upon the source voltage applied to the bridge and since also the conductive component of the admittance is small compared with the susceptive component, error in this measurement may account for the discrepancy. On the whole, however, the agreement between the measured and calculated NEP is sufficientlygood to indicate that the analysis of the pyroefectric detector given in Part I1 is adequate to account for its behavior and to show what steps are needed to improve the performance still further. In addition to improving the responsivity by improving q, the Johnson noise might be reduced by increasing the resistivity of the material. This might be achieved either by using improved TGS with smaller dielectric loss or by using other pyroelectricmaterials with higher resistivity. Thus preliminary measurements with Li2S0,.H20 detectors indicate that the resistivity of this material is
278
E. H. PUTLEY
about an order of magnitude greater than the TGS we have been using. If the resistivity could be increased two orders of magnitude, the Johnson noise would be reduced below the temperature noise, but this again could be reduced by improvement in the design of the thermal circuit, so that at low frequencies it should be possible to approach within a factor of two or three the NEP of an ideal background-radiation-limited detector. If this performance were achieved, the pyroelectric detector would have a higher detectivity than any other room temperature thermal detector.
b. High Frequency Performance
It is clear from Fig. 3 that although by the use of a frequency equalizing amplifier the overall responsivity can be held at a constant level to frequencies very high compared with l / or ~ l ~/ ~the ~ ,NEP will start falling off above a few hundred hertz. The usefulness of frequency equalization will therefore depend on the extent to which a deterioration in NEP is acceptable. This consideration is one factor which will determine the upper frequency limit. In addition to this there may be other limiting factors. Thus users of the total energy detector in its fast mode of operation',' ',19 have encountered mechanical resonances near 100 kHz which have determined the upper-frequency limit for their detectors. These resonances appear to be associated with elastic compression waves propagating along the length of the detector. Careful tests with detectors constructed as described in Section 6 failed to detect this mode of vibration and, as Fig. 10 demonstrates, a useful performance was
Detection at 10.6 1
0
1 Time ( p s e c )
2
FIG.10. Comparison of the response of a pyroelectric detector and of a Zn:Sn-doped Ge detector to Q-switched CO, laser pulses. (After Kimmitt et ~ 1 . ' ~ )
6. THE PYROELECTRIC DETECTOR
279
still obtained when the frequency equalization was extended to 2 MHz (corresponding to an effective response time of 100 nsec). The construction used appears to suppress the transverse compression resonance, but if this type of resonance occurs along the direction normal to the receiving aperture of the detector, the resonance frequency will be of the order of 100 MHz. Thus far, measurements have not been made at this frequency, so that the existence of this mode cannot be confirmed. Acoustic measurements at lower frequencies have revealed the existence of what appear to be flexural resonances in the 10-20 kHz region. These lower frequency modes do not seem to be excited by pulsed radiation sources, so that with the type of detector described here the limit set by elastic resonances is probably not less than 100 MHz. As an indication of the sensitivity obtainable, the results shown in Fig. 10 were obtained using a Li,S04.H20 detector 7 mm in diameter and 50 p thick with a responsivity of 3 V/W over the frequency range 20 Hz to 2 MHz. The total noise output over this bandwidth was 15 mV rms. Hence a pulse of a few milliwatts peak power could be detected. 8. COMPARISON WITH OTHERDETECTORS
The last two sections have given a detailed account of the construction and performance of the pyroelectric detector constructed at RRE. Although the performance described probably does not represent the ultimate attainable, it is typical of the state of the art for this type of detector, and it is beginning to compare favorably with other types of detector. The NEP attainable at low frequencies is about W, or perhaps slightly better,and this is comparable with the values reported by other workers?,"-' When used as a fast detector, effective response times as short as 100 nsec have been achieved, although it appears that to achieve this result, some care is necessary in the design of the detector element to suppress elastic resonances, In Fig. 11 the NEP of the RRE pyroelectric detector is compared with that ofother detectors operating at room temperature. As there is some uncertainty as to the relation between NEP and area, the results are not normalized to unit area but detectors of area similar to that of the pyroelectric detector have been chosen. The other detectors are all commercially available ones and the performances shown were obtained from the manufacturer's specifications. In Fig. 12 the frequency dependence of the NEP's for these detectors is shown. The pyroelectric detector was operated with a frequency equalizing amplifier, and the deterioration in the NEP at 1 kHz is due to amplifier noise contribution at the higher frequencies. The use of frequency equalization is not advantageous with the Golay cell or thermistor bolometer, nor is it usually required with the photoconductive detectors, so that for the other detectors the falling off of NEP is related to the response time of the detector.
280
E. H. PUTLEY
0.I
I
10
10'
lo3
lo4 10
I Wavelength ( p 1
A (mm)
FIG.11. The detectivity (l/NEP) of a pyroelectric detector compared to those of a Golay cell, a thermistor bolometer, and room temperature PbS and InSb photoconductive detectors. The areas of the detectors compared are given on the figure. The detectivity of an ideal thermal detector at room temperature is shown for comparison.
The data presented in Figs. 11 and 12 show that the pyroelectric detector compares favorably in NEP with the thermistor bolometer and the room temperature InSb photoconductive detector, but is inferior to that of the Golay cell and the PbS detector. The frequency response of the pyroelectric detector is appreciably superior to that of the other thermal detectors. In common with other thermal detectors, the spectral response of the pyroelectric detector extends to very long wavelengths; in fact, a useful performance can be obtained at submillimeter and millimeter wavelengths (although a form of construction more compatible with waveguide circuitry should be adopted for use beyond 1 mm wavelength2'). Results obtained in the submillimeter region with the 337-p CN maser are shown in Fig. 13. 21
D. J. White, J . Appl. Phys. 35,3536-3542 (1964)
6. THE PYROELECTRIC DETECTOR
281
I20 CPY PbS
I06
10
lo3
lo4
Frequency (Hz)
FIG.12. The frequency dependences of the peak detectivities of the detectors shown in Fig. 11.
The results shown in Figs. 11-13 thus demonstrate that where a simple uncooled detector is required the pyroelectric detector has much to commend it. For wavelengths longer than 3 p it has a better sensitivity than most detectors. Its effective response time compares favorably with the photoconductive detectors, while its spectral response can only be matched by liquid helium cooled photoconductors. Where robustness rather than high sensitivity is required, very simple detectors can be made from readily available materials,22 but higher-performance pyroelectric detectors are now becoming available commercially.22" W. W. Duley, J . Sci. Instr. 44,629-630 (1967). ""Manufacturers producing pyroelectric idfrared detectors include : Mullard, London, England ; Barnes Engineering, Stamford, Connecticut ; and Prtcitechnique Dauphin6 Grenoble, France.
22
282
E. H. PUTLEY
FIG.13. Response t o emission from a C N maser. The rcsponse of a pyroelectric detector (lower trace) is compared with that of an InSb submillimeter detector (upper trace). The pyroelectric detector responds to both the visible and the submillimctcr emission from the discharge. but the InSb detector responds only to the submillimeter radiation. This is demonstrated by the use of various filtcrs with the detectors as follows: ( I ) Pyroelectric: n o filtcr: InSb: nu filter. (2) Pyroelcctric: black polythene excluding visible; lnSb : 110 filter. (3) Pyroelectric : glass filter excluding submillimeter; InSb : no filter. (4)Pyroelectric : detuning laser cavity causes double pulsing from laser which pyroelectric detector is too slow to follow. (5) Pyroelectric: no filter; InSb: black polythene excludirig visible. ( 6 ) Pyroelectric: no filter; InSb: clear glass excluding submillimeter.
6. THE PYROELECTRIC DETECTOR
283
Appendix. Electrode Geometry
The electrode configuration assumed so far is that shown in Fig. 14(a), in which the pyroelectric axis is normal to the receiving area of the detector and a partially transparent or absorbing electrode (“face electrode”) is applied to the front surface of the detector. A second configuration, shown in Fig. 14(b), is also possible. In this the pyroelectric axis lies in the plane of the receiving area. Electrodes are applied along the edges of the plate normal to the pyroelectric axis (“edge electrodes”). To compare the two configurations, consider the Eqs. (28H31)for PN, the noise equivalent power associated with the various noise sources. These must first be rewritten to distinguish between A,, the area of the electrode, and A,, the receiving area. Here d is the distance between the electrodes, and for the face electrode configuration AE = AR. Thus we have pN, temp PN. Johnson
= (l/r)(4k T2)1’2 (g)’’2(AR)1/2
(A281
= (1/V)(4kT)1’2(c‘/pp1i2)(AEd)’i2 7
Incident radiation1
I
I
I+ 1 axis
Incident radiation
I electrodes
Pyroelectric axis
FIG.14. Electrode geometries for (a) face electrode, and (b) edge electrodes.
(A29)
284
E. H. PUTLEY
PN.amp current
=
(1h) Ai(c’/~)d
6430)
PN,ampvoltape
=
(l/q)(w AVA)(C’E’E/P)AE.
(A31)
9
Equations (A28) and (A29) are identical to Eqs. (28) and (29), respectively, so that changing the electrode configuration does not alter the temperature or Johnson noise limited value for PN.However, for the same size and shape of detector with edge electrodes d is larger than with face electrodes, and A , is smaller. Hence for edge electrode PN,ampcurrent will be larger and PN,ampvoltage will be smaller than for face electrode. Referring to Fig. 6 shows that at high frequencies, PN, will always limit the performance. Hence there would appear to be some advantage in using edge electrode detectors for high frequency operation. The physical reason for this advantage of edge electrodes is that the electrical capacity of the element is less by a factor which with typical dimensions could be as much as lo4. Since the capacity of a typical face electrode pF, detector is about 50 pF, the capacity of the edge electrode device, 5 x is well below the stray and amplifier input capacities. Hence the improvement with the edge electrode configuration will not be as large as expected from the simple geometry. Equation (3 1) can be written PN,arnpvoltage
= (l/q)(wc AVA)c’d/p‘
(A31‘)
Onlyif the reduction in C (taking into account circuit capacitance) is greater than the increase in d will the edge electrode arrangement be beneficial. With the dimensions we have been considering this appears to be unlikely.
Note Added in Proof Development of the pyroelectric detector is continuing. It is now possible to obtain detectors from commercial sources with NBP’s a factor of 2 to 3 smaller than the value shown in Figs. 3, 11, and 12. This improvement is largely the result of improved fabrication techniques since so far no pyroelectric material superior to TGS has been found. Another factor contributing to the improved performance is the development of better FET’s. The best available now have a voltage noise about one quarter of that shown for the BFW.ll in Fig. 5 and probably also have a somewhat smaller current noise. As a consequence, the dominant noise source in TGS detectors at frequencies up to about 1 kHz is Johnson noise. At higher frequencies, amplifier voltage noise will still be the most important, but with the best available amplifiers, an NEP of about 7 x lo-’ W Hz- 1/2 should be achievable at 1 MHz. There is at present considerable interest in pyroelectric materials. Detailed measurements at RRE on Lipso,. H,O have shown that the best NEP’s obtainable for detectors fabricated from this material are a factor of 2 to 3
6. THE PYROELECTRIC DETECTOR
285
more than the best TGS detectors. has reported encouraging results with strontium barium niobate crystals. Although this material has a larger cm-2 O K - ’ ) , it has a much larger pyroelectric coefficient (-1.1 x dielectric constant (- 1700) and a lower resistivity ( lo9 ohm cm) than TGS. Hence in some low frequency applications i t could be superior to TGS but it appears inferior to TGS for higher frequency applications. Since the best TGS detectors are Johnson noise limited, higher resistivity material is required to obtain further improvement in the NEP. One possible way of obtaining this is the development of better quality TGS having lower dielectric loss. Another approach is to look for newer materials (perhaps among the niobates or tantalates) having higher resistivities. Since the dielectric loss or resistivity is probably determined by impurities or imperfections in the crystal, this search is not likely to succeed unless a systematic study of the preparation and properties of likely materials can be undertaken. Materials which have been studied recently at RRE include EDT, DKT, and GASH, all of which are inferior to TGS. has also measured these, obtaining results in good agreement with our own. Since the NEP of the best pyroelectric detectors is between one and two orders of magnitude worse than that of an ideal room temperature thermal detector, there is a good chance that significant improvement in the performance of pyroelectric detectors will be attained in the near future. Several groups have reported using a pyroelectric detector in a homodyne or heterodyne configuration with a laser local oscillator. Thus Gebbie et aL2’ discuss the use of a TGS detector with a CN maser (337p), Leiba26 has used a TGS detector with a C 0 2 ( 1 0 . 6 ~laser, ) and Abrams and Glass27 have described an experiment with a strontium barium niobate detector and C 0 2 laser. Recent work at Barnes has been discussed by Beerman,28while AstheimerZ9 has described a thermal imaging system using a TGS detector. TGS detectors are being successfully used in submillimeter Fourier transform spectrometers (N. W. B. Stone, private communications) and they are beginning to appear in some commercial instrument^.^' N
A. M. Glass, Appl. Phys. Letters 13, 147-149 (1968). Hadni, Opt. Comm. 1,251 (1969). ” H . A. Gebbie, N. W. B. Stone, E. H. Putley, and N. Shaw, Nature214, 165-166 (1967). 26 E. Leiba, Compt. Rend. 268, 31 (1969). R. L. Abrams and A. M. Glass, Appl. Phys. Letters 15,251-253 (1969). ’* H . P. Beerman, ZEEE Trans. Electron Devices 16, 554-557 (1968). 29 R. W. Astheimer, Photogr. Sci. Eng. 13, 127-133 (1969); R. W. Astheimer and F. Schwarz, Appl. Opt. 7, 1687-1695 (1969). 30 For example Block FTS-14, Fourier transform spectrometer. 23
” A.
*’
This Page Intentionally Left Blank
CHAPTER 7
Radiation Thermopiles Norman B . Stevens
I . INTRODUCTION . I1 .
111.
IV .
V.
. . . . . . . . . . . . . . . . . . . . . . . . .
1 . Historical Background . . . . . . . . . . . . . 2 . Thermopile Radiation Detectors THEORETICAL BACKGROUND . . . . . . . . 3 . Seebeck Coefficient . . . . . . . . . 4 . Peltier Coeficient . . . . . . . . . 5 . Thomson Coeficient . . . . . . . . . 6 . Equations of Eyuilibrium . . . . . . . 7 . Consideration of (T,, - To) . . . . . . . 8 . Parameters Affecting Responsivity . . . . . 9 . Materials Criteria . . . . . . . . . THERMOPILES AS RADIATION DETECTORS. . . . 10. De.yign Criteria . . . . . . . . . . 11 . Device Figure fffMerit . . . . . . . . 12. D* as a Criterion of Merit . . . . . . . 13. M , as a Criterion . . . . . . . . . 14. Profile . . . . . . . . . . . . 15. Spectral Response . . . . . . . . . PROPERTIESOFTHERMOPILE RADIATION DETECTORS. 16. Bulk Material Devices . . . . . . . . 17. Thin Film Devices . . . . . . . . . 18. Evaporated Thermopile Arrays . . . . . . CONCLUSION . . . . . . . . . . . . LISTOF SYMBOLS . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. 287 . 287 . 288 . 289 . 290 . 290 . 291 . 292 . 294 . 296 . 297 . 299 . 299 . 299 . 301
.
301
. 302 . 302
. . . . . .
304 305 307 312 317 317
I . Introduction 1 . HISTORICAL BACKGROUND Thermocouples and thermopiles have been employed since shortly after the discovery of infrared radiation by Sir William Herschel‘ in 1800. Report was made as early as 1835 of a thermopile fabricated and used by Melloni’ W . Herschel. Phil . Trans. Roy . Soc. (London) 90. 284 (1800); R . A . Smith. F. E. Jones. and R . P. Chasmar, “The Detection and Measurement of Infrared Radiation, ” p . 1. Oxford Univ . Press, London and New York. 1957. M. Melloni. Ann. Chim. Phys . (2) 60.418 (1835); Smith et a/.,’ p . 2.
287
288
NORMAN B. STEVENS
as a temperature sensor for detecting the presence of radiated heat. The early experimenters studying infrared radiation using thermocouples as detectors were not only utilizing the very recently discovered Seebeck effect (1822), but their work falls into appropriate perspective when it is noted that the 12R Joule heating was not even recognized until 1844.3 In 1834 Jean C. A. Peltier4 discovered the heating or cooling of the junction of a current-carrying circuit of two dissimilar metals, the effect depending upon the polarity of the electric current. It remained for William Thomson (Lord Kelvin) to recognize the temperature dependence relationship between the Seebeck (01) and Peltier (H) coefficients, now designated as the second Kelvin relation :
n = Ta,
(1)
where T is the absolute temperature, O K . It was also William Thomson who recognized and predicted the Thomson effect on thermodynamic grounds, and observed it experimentally in 1853.5 Subsequent to the formulation of the second Kelvin relation, practical applications of these discoveries were largely lacking other than for making temperature measurements. With the advent of modern materials research, however, materials of greater utility were developed both for temperature measurement and refrigeration. The status of present day materials development is covered in excellent detail by Cadoff and Miller.6
2. THERMOPILE RADIATION DETECIMS It is important at the outset to describe what is meant by a radiation thermopile. The device includes a collector or absorber of radiant energy, usually for the infrared wavelength region. The collector exhibits a temperature rise over the detector ambient or reference temperature as a result of the absorbed radiation. This characteristic of utilizing a temperature rise as an intermediate process between radiation absorption and electrical response is shared with the radiation bolometer, and classifies it as a thermal rather than a quantum detector. The bolometer is distinguished from the thermopile by the mechanism employed to measure the temperature increment of the collector. Bolometers have a relatively large temperature coefficient of resistance and require a bias current to detect this change of resistance. The thermocouple generates a voltage due to the Seebeck effect, obviating the need for stable bias circuitry. Other thermally variable properties of materials
’ P. H.Egli, “Thermoclectricity,” p. 4. Wiley, New York, 1958. I . B. Cadoff and E. Miller, “Thermoelectric Materials and Devices,” p. 4. Reinhold, New York, 1960. S. P. Thomson, “Life of Lord Kelvin,” Vol. 1, p. 317. Macmillan. London, 1910. See Cadoff and Miller: p. 55.
7. RADIATION THERMOPILES
289
are useful for thermal detectors of radiation (e.g., Golay cells and pyroelectric detectors), but the thermopiles and bolometers enjoy the greatest utility. Two types of thermopile are extensively employed. The first is a fabricated, bulk material device, usually made with fine wires and provided with a thin, black radiation absorber. The second is the thin film thermopile made by vacuum evaporation of the components, permitting the use of photoetch techniques and the attendant high precision in the device assembly. Although this may appear to be an artificial classification, it is a useful one, since the two kinds of device exhibit quite different properties. The extremely small connections and thermal elements provided by evaporation permit the design of devices covering a wide range of impedance and time constant. This allows selection of an impedance which falls near the optimum impedance of modern amplifying transistor circuits. It is true that with careful amplifier development the low impedance fabricated devices are Johnson noise limited, but the circuit usually involves a costly transformer with its attendant magnetic pickup and frequency response problems. Harris7 in 1934 made use of vacuum evaporation techniques in making thermocouples and thermopiles, and developed the theory for the proper design of a couple. He utilized ac amplification and prepared an eightjunction couple. Slightly later (1945) Roess and D a c d adapted the evaporated thermopile design to the requirements of infrared spectroscopy. This chapter will be devoted to consideration of radiation detectors utilizing the Seebeck effect. The operation of these thermoelectric devices is described by much the same theory that applies to refrigeration piles and temperature measuring couples. The theory will be presented briefly and relevant formulas for the radiation couple or thermopile will be given. The character and magnitude of the noise encountered in such a radiation detector will be considered, and finally, typical present day thermopiles of both the bulk material and evaporated types will be shown and properties will be described. 11. Theoretical Background
The conduction electrons in a metal or semiconductor possess thermal energy in addition to electric charge. The thermal energy can be transported physically with the charges either up or down a thermal gradient by the application of an appropriate electric field gradient. Similarly, application of a thermal gradient can transport electric charge along an electric field gradient of either polarity.
’ L. Harris, Phys. Rev. 45, 635 (1934). L. C. Roess and E. N. Dacus, Rev. Sci. Instr. 16, 164 (1945).
290
NORMAN 8 . STEVENS
COUNTER EMF FIG.1. Seebeck effect.
For thermocouples it will be seen that the three thermoelectric effects, designated Seebeck, Peltier, and Thomson, are not equally relevant. The quantities are defined as follows:
3. SEEBECK COEFFICIENT When two metals comprisc a circuit (Fig. 1) and the junctions of these metals are at differing temperatures (i.e., due to the absorption of incident radiation), an electric current flows. Insertion of a counter emf will cancel the current flow, and the magnitude of this emf is the Seebeck voltage. More specifically, the Seebeck coefficient is defined as CL
= lim
AVIAT
=
dVIdT,
AT40
where AV is the emf between the two junctions and AT is the temperature difference between the junctions. The polarity of A V will reverse with reversal of AT. The Seebeck coefficient c( is also known as the thermoelectric power. 4. PELTIER COEFFICIENT
When the circuit of two dissimilar metals is traversed by an electric current, heat is exchanged into or out of the circuit at the two junctions as shown in Fig. 2. Considering first junction number 1, the rate of heat exchange at the junction is proportional to the magnitude of the current as
291
7. RADiATION THERMOPILES
I
dQ HEAT IN = -
dt
:
TI
FIG.2. Peltier coefficient
defined in the following equation :
nI
= dQ/dt
(3)
where the proportionality constant I'l is the Peltier coefficient, I is the electric current, and d Q / d t is the time rate of heat exchange. Reversing the polarity of the current reverses the direction of heat exchange. That is, with one direction of current, heat is evolved at one junction and absorbed at the other junction, while reversing the current direction interchanges the heat exchanging roles of the two junctions. 5 . THOMSON COEFFICIENT
In the course of Thomson's work leading to the formulation of the relationship between Seebeck and Peltier effects the existence of a similar effect in a single homogeneous medium was predicted. If a material carrying electric current possesses a thermal gradient, as shown in Fig. 3, heat is absorbed or evolved reversibly at a rate defined by the equation dQJdx = 7 1 d T / d x .
(4)
Here d Q / d x is the heat absorption rate per unit length, and is positive when I and dT/dx are in the same direction and t,the Thomson coefficient, is positive.
292
NORMAN 6. STEVENS
db dx
dT
1-7- dx
dx
Th
6 =J r r d T TC
FIG.3. Thornson coefficient
It should be recognized that in a circuit of dissimilar conductors in which there are temperature gradients there will be generated emf's due to Seebeck and Thomson effects. The sum of these emf's is the thermal emf of the circuit, or the thermoelectric force E . The Seebeck coefficient or thermoelectric power a is the rate of change of the thermoelectric force E with respect to temperature T , or a = dE/dT, (5) or, expressed in terms of a two material junction or circuit, =
dEiJdT.
(6)
Utilizing the second Kelvin relation [Eq. (I)], this may be expressed as
ll,, = T a l z = T d E , , / d T .
(7)
Before turning to the relevance of these equations to thermopile design it may be noted that the Kelvin relations were derived originally from considerations based upon the second law of thermodynamics. It was recognized by Onsager' that irreversible phenomena were nonetheless present, and more rigorous proofs of Kelvin's relations were sought. Those considerations are well developed and explained in the work of Lucke," and a derivation of Kelvin's relations is presented by Gray" and by Jaumot.
'
6 . EQUATIONS OF EQUILIERIUM Turning now to thermocouple design, it may be noted that most radiation thermocouples are basically similar to the configuration shown in H . J. Goldsmid, "Applications of Thermoelectricity," p. 5. Wiley, New York, 1960. W. H. Lucke, A Brief Survey of Elementary Thermoelectric Theory, US.Naval Res. Lab., Washington, D.C. (NRL Report 5888). May 1963. '' P. E. Gray, "The Dynamic Behavior of Thermoelectric Devices," p. 107. Technology Press of MIT, Cambridge, Massachusetts, 1960. F. E. Jaumot, Jr., Proc. I.R.E. 46,538 (1958). I"
''
7. RADIATION THERMOPILES
293
FIG.4. Thermocouple heat flow schematic
Fig. 4. Here the heat rate balance equation is Qh
=
QGT,~
- 3QJ + QII,
+ QGT,~f
(8)
where Q h is the rate of heat absorption into the junction from the net radiation imbalance; QCT,,and QcT,2are the rates of heat conduction down arms 1 and 2; and are the rates of heat evolution due to Thomson effect in arms 1 and 2 (half appears at the cold sink); QJ is the Joule Thomson heat generation rate in the thermocouple portion of the circuit (due to the presence of two arms, half is absorbed in the cold sink); ando, is the Peltier heat generation rate by the electric current at the hot junction. It is evident that QG+ depends upon the thermal conductance of the arm. This in turn is related to the area A, length 1, and specific thermal conductivity K , so to a first approximation (for small A T )
e,, e,,
QGT = (KA/l)(Th
-
TO).
(9)
Similarly, Qr depends upon the current I and the Thomson coefficient T , and for small temperature differences the rate of evolution of Thomson heat is
Q* =
-
qJ),
(10)
of which half affects the heat balance of the hot j ~ n c t i o n . 'In ~ the case in which I and Th - To are both small the Thomson contribution becomes a second order effect and hence may be neglected. Even in the case of power ' ~ these reasons generating thermocouples the effect is only about 1 5 % ~ For the influence of will not be considered further. l3 l4
See Cadoff and Miller," pp, 28-30. See Gray,' pp. 28 and 39.
294
NORMAN B. STEVENS
The Joule heating QJis simply due to electrical dissipation in the arms, and is given by =
QJ
12Re,ec.
(11)
Half of this thermal power appears at the cold sink’2 as noted in Eq. (8). The magnitude of Relec is composed not only of R , + R,, but also must include a dynamic resistance term due to the Peltier heating of the hot junction, induced by the electric current.” This dynamic resistance R , is always positive, so the temperature change induced by the radiation at the hot junction is always reduced by this Peltier effect. Admittedly, in a thermopile operating into a large load ( R L )the current will be very small and R , will, in practice, be negligible. Its magnitude is
R,
=
nZRT/T= n2/G,IT:
(12)
where RT is the thermal resistance and GT the thermal conductance of the hot junction. Thus the electrical resistance of the circuit becomes
R, should rigorously include a component due to the Thomson effect. It is small, however, so will not be considered in its effect on R,. With a radiation thermopile operating into a large load the I Z R heat source may be neglected, and this permits us to further simplify Eq. (8) by dropping the term QJ. The term Q n [Eq. (S)] is the Peltier heat generation rate at the hot junction by the electric current, and its magnitude is Qn =
nlzi = Z l Z i T h .
(14)
Collecting terms, we may rewrite Eq. (8) as
7. CONSIDERATION OF (T,
-
To)
It will now be illuminating to consider what enters into the determination of the quantity Th - To, or in general, AT. This development is given in If a quantity of heat Q is absorbed by a mass greater detail by Holter et of material, its temperature rise is governed by the equation C, = d Q / d T ,
(16)
’’ See Smith, et a/., ’ pp. 61-63, l6
M. R. Holter, S. Nudelman, G. H. Suits, W. L. Wolfe, and G. J. Zissis, “Fundamentals of Infrared Technology,” p. 228 Macmillan, New York, 1962.
295
7. RADIATION THERMOPILES
where C, is its thermal capacitance. Similarly, if a length 1 of material of area A experiences an overall temperature difference AT, its rate of heat conduction is dQ/dt
=
- K A dT/dx x -(KA/f)AT
(17)
where K is the specific thermal conductivity. If a thermally isolated mass experiences a temperature increment and is connected to a thermal conductor, the rate of loss of thermal energy is obtained using Eqs. (16) and (17): dQ/dt
With T
= CT
dT/dt = - K A dT/dx.
(18)
= Th,Eq. (18) becomes CTdTJdt = - K A AT/l.
Noting that AT
E
(18')
T,, - To and that To is time-independent, we may write
CTd(AT)/dt= - ( K A / I ) AT = -AT/RT
=
-ATGT.
(19)
This can be rewritten as a differential equation
d(AT)/dt + AT/RTCT = 0.
(20)
The solution to this equation is
AT
=
(AT),exp( - t/RTCT).
(21)
If, however, radiant power P is absorbed, Eq. (20) becomes
d(AT)
cT
KA
dti - - 1- A T = P ,
where P is constant for the dc case or P = Podmtfor the sinusoidal case. The solutions in these two cases are
AT
=
RTP
and
However, the passive case of a thermal capacitor and conductor absorbing thermal radiation and exhibiting the familiar exponential temperature distribution developed above can be used in the case of the thermocouple only when the zero electric current case is realized. If this is not the case and current I is generated in a couple circuit by absorption of radiation, the hot junction is cooled by the Peltier effect. This temperature increment is then
296
NORMAN B. STEVENS
But we know that 1 = E / R = a12A T / R = RTPa,2/R
(26)
for the dc case. Thus
A% = RT2ci~2 TP/R, (27) where R is the circuit electrical resistance, which to B first approximation is simply the resistance of the two arms plus the external circuit. Due to this current there is an additional cooling effect A T due to the Thomson effect in the two arms, where
A T = RTQ = $IRT A T ( T I Here again A T
=
+~2).
(28)
RTP in the dc case, and f
=
R,Palz/R,
or
AT
+
=
$(R,Pal2/R)R~P(?, T ~ ) R T
=
RT3p2cxI2(Tl+ z 2 ) / 2 R .
(30)
At first P 2 dependence seems surprising, until it is remembered that the temperature increment to the Thomson effect is dependent upon both the junction temperature increment and the current induced by that temperature increment. Clearly, if we include this Thomson effect, we have an unwieldy
(31) AKffective = RTP - A& - AT,. The solution of the resulting differential equation is not of immediate importance for the case of radiation thermocouples operating into large loads, where both I and AT are small, as noted above. Again it should be noted that this is not the case in thermal refrigeration or power generating devices. 8. PARAMETERS AFFECTING RESPONSIVITY
The responsivity PA of a thermocouple is defined as the open circuit output voltage divided by the input, in radiant watts. We may write from Eqs. (2), (23),and (24) that for this case the steady-state voltage will be AV
=
a12 AT = MlzRTP,
(32)
while for the sinusoidal case we obtain
(33)
7. RADIATION THERMOPILES
297
The power absorbed by the junction has simply been designated P, or Podwt,above. However, the incident radiation Pi contained within the collector surface area normal to the radiation angle of incidence will in fact be larger by that actually absorbed because the emittance E of the absorbing surface is less than unity ; P = EPi. (34) For any reasonably good absorber E will be between 0.9 and 1.0 over the wavelength band of interest. It must be recognized that any window loss will generally contribute a greater degradation than the loss due to nonblackness of the absorber. The responsivity W then becomes
W
== Nl,R=P/Pi =
CtlzER,
(35)
for the steady-state case, or more generally
W = ctl2RT~/[1 + 02RT2CT2]1i2
(36)
9. MATERIALS CRITERIA The performance of a radiation thermocouple is enhanced when - To is maximized with respect to the electrical circuit noise. It is desirable to minimize the electrical circuit resistance while minimizing the thermal conductivity of the two arms of the couple. These are contradictory requirements in view of the Wiedemann-Franz law” relating the thermal conductivity K and the electrical conductivity (T :
V/oC (37) (with L the Lorentz number). This leads naturally to the well-known criterion or figure of merit for materials in which a maximum value of a2rr/K is sought. It is defined” for two materials as follows: K f a T = L x 2.45 x lo-’
+
= ~ t f 2 [ ( K ~ / o ~ () ’K/ ~ / o ~ ) ” ~ ] - ~ .
(38) To have a high figure of merit Z12,the following conditions must obtain: Zl2
1. Thermal conductivity should be small compared to eiectrical conductivity. Usually the factor K/oT, the Lorentz number, is not unrelated to the Seebeck coefficient, so materials with larger values of L tend to exhibit large Seebeck coefficients. 2. The Seebeck coefficient should be large. ” See
Smith, et d . , l p. 7 6 . See Cadoff and Miller,” pp. 21 and 55. It is important to note that this thermoelectric figure of merit is defined in terms of output power delivered into an optimum load resistance, rather than the open-circuit output voltage which enters directly into the definition of the responsivity. The materials parameters affecting this latter quantity were given in Eq. (35).
298
NORMAN 9.STEVENS
Turning briefly to the optimization of the lead configuration, it is known that the thermal conductance of the two arms should be nearly equal. Expressed differently, if the lengths 1 be equal (as is often most convenient) then the cross-sectional areas should be adjusted so the material with greater thermal conductivity will have a correspondingly smaller area to equalize the thermal conductance in the two arms. With the thin film deposited thermopiles discussed later, the thermal conductivity and Seebeck coefficients may not be those published for bulk materials. These properties for deposited thin films may in fact be quite different. Harris and Corrigan” found that for antimony, e.g., the resistivity increased from 58 to 95 x lo8 ohm cm and the Seebeck coefficient declined from 45 to 36 pV “ C - ’ in vacuum deposited layers of 15,350 and 1000 A, respectively. Thermoelectric materials criteria having an influence on a2u/K have been considered in detail by Ioffe.20 His development was based upon the influence of carrier concentration, and did not consider the influence of change in effective mass or mobility from material to material. These material properties and influences are reviewed and summarized by Cadoff and Miller2’ and Egli.22 Ioffe’s conclusions with respect to carrier concentration are of some interest, and are listed here: 1. The Seebeck coefficient CI is inversely related to the carrier concentration by the relationship CI
=W q N ,
(39)
where C,is the specific heat of the charge carriers, N is the number of carriers, and q the charge of each carrier. It has been noted by HadniZ3that for semiconductors N is small compared to metals, giving a larger CI. 2. The electrical conductivity u is approximately proportional to the carrier concentration. 3. The thermal conductivity K consists of a concentration invariant lattice term and an electronic or carrier dependent term, increasing, as does the electrical conductivity, with concentration. 4. Combining these trends in the a2u/K relationship yields a broad maximum at carrier concentration between 3 x 10’’ and 3 x 1019cm-3. l9
L. Harris and F. R. Corrigan, J . Phys. Chem. Solids 26, 307 (1965).
’” A. F. loffe, “Poluprovodnkovye Termoelementy,” Academy Sciences, USSR, 1956 [English
’’ 22 23
Transl. ; “Semiconductor Thermoelements and Thermoelectric Cooling,” Infosearch Ltd., London, 19571. See Cadoff and Miller: pp. 76-83. See Egli,3 pp. &lo. A. Hadni, “Essentials of Modern Physics Applied to the Study of the Infrared,” p. 296. Macmillan (Pergamon),New York, 1967.
7.
RADIATION THERMOPILES
299
111. Thermopiles as Radiation Detectors 10. DESIGNCRITERIA We are now in a position to define the desired properties of an ideal thermopile : 1. Response should be maximum for a given rate of radiant energy absorption, i.e., the responsivity 9 in V/W should be a maximum. 2. The time constant of the device in its response to a pulse of radiation should approximate the minimum dictated by the application, or the design should permit selection of the required time constant. 3. The electrical impedance, which generates Johnson noise, should be designed to provide maximum system signal-to-noise ratio. No simple rule of thumb applies here, since the kind and impedance of the amplifier selected and the electrical noise characteristics of the environment all must be considered. 4. The spectral responsivity should be constant within the wavelength region of interest. 5. The response should be uniform over the entire sensitive area, i.e., the profile should be flat. 6. Secondary properties of practical importance include the following : (a) temperature coefficient of responsivity, (b) resistance to mechanical shock and vibration, (c) permissible temperature extremes, (d) life or permanence of the device as packaged, (e) convenient shape and size of the device as packaged, and (f) electrical impedance compatible with amplifier requirements. These numerous properties are clearly not independent, nor are they simply related. In designing a thermopile for a specific application one generally must maximize responsivity, select a minimum time constant, and provide an impedance near the optimum for a minimal system noise. The other properties must be known to ensure that they are compatible with the environmental demands of the application. Clearly one must first select a pair of materials for the thermocouple which give a maximum figure of merit. Beyond this, the construction details must be determined. As noted earlier, two general types of thermopile are in use today. The first is made with wires of active, bulk material, i.e.,antimony and bismuth, or other alloyed materials, The other utilizes photoetch techniques to provide a vacuum deposited device. In Part IV examples of both types will be described.
11. DEVICEFIGURE OF MERIT In this section we will consider some useful device figures of merit. Although the evaporated devices will be considered, the results are equally applicable
300
NORMAN 8.STEVENS
\
SUBSTRATE FIG.5. Evaporated-thermopile schematic.
to the bulk material designs. Before considering various figures of merit it will be useful to describe a conventional evaporated thermopile, as shown schematically in Fig. 5. Four couples in series are shown, with a sensitive area A = H, x W,. The active metals are evaporated with a width w to a nominal thickness t (adjusted to provide equal heat loss through each side of the couple). In the following equations several reasonable assumptions are made: (1) The major loss of energy from the sensitive area is through the active arms, i.e., radiant heat loss is not large. (2) Conduction loss through the substrate or to a surrounding gas is negligible. (3) Temperature equalization across the sensitive region W, is realized in a time small compared to the device time constant T ~ . (4) The Wiedemann-Franz ratio for the materials is invariant with respect to thickness t. The following empirical relationships describe the properties of this configuration : responsivity
w rx: l/W,t;
(40)
7 . RADIATION THERMOPILES
301
impedance (l/Kt)Nh,
where Nh is the number of hot junctions (four, as shown in Fig. 5 ) ; and time constant
where A is the sensitive area. Before combining these factors into a figure of merit we wish to examine two criteria proposed by Jones,24 D* and M 2 .
12. D” AS
A
CRITERION OF MERIT
The well-known criterion D* proposed by R. Clark Jones has justifiably enjoyed widespread use for comparing detectors. This may be defhed for unit electrical bandwidth as
The multiplying factor A‘‘, permits comparison of detectors of different areas. Underlying the validity of this figure of merit is the assumption that the noise is dependent upon A’/’. In some thermopiles this A’” dependence of the noise is not realized. Examining the schematic of Fig. 5 we see that we can increase the area by inserting a high thermal conductivity metal, e.g., silver, in series with the hot junction, thereby increasing W,. This change, however, does not significantly change the device impedance ; hence the Johnson noise is unaltered even though area has been changed. A similar condition is described by Smith et aLz5 Here, clearly, D* may not be used unambiguously. One additional comment is that, aside from the above precaution to be observed when invoking the use of the D* for thermopile detectors, D* fails to designate the time constant of the device. This parameter must always be one of the boundary conditions to be considered in a thermopile design.
13. M2
AS A CRITERION
Another proposed criterion by Jones,26 M,, is based upon the Havens limit.27*28 It takes the important parameter of time constant into account, R. C. Jones, Proc. I.R.E. 47, 1495 (1959). See Smith et al.,’ p. 251. 26 See Jones,24 p. 1499. 21 R. J. Havens, J. Opt. SOC. Am. 36, 355(A) (1946). 2 s P. W. Kruse, L. D. McGlauchlin, and R. 3.McQuistan, “Elements of Infrared Technology,” p. 385. Wiley, New York, 1962. 24
2s
302
NORMAN B. STEVENS
and is defined as:
M 2 = 6 x 10-" (W seccm-')D,*/rA'2
(44) where Om*is the maximum value of D* with respect to frequency and td is the detector time constant. The constant M , is based upon a Havens limit thermal detector which involves viewing the detector as a thermal engine with 10% efficiency. For this assumption Havens found that the minimum energy (not power) at the receiver to give a unity signal-to-noise ratio was independent of time for a response time shorter than 40 msec, and proportional to the square root of the time constant for longer times. For a 40 msec thermal detector the Havens limit is D* = 5.6 x lo9cm Hz"* W - I . This is about one-fourth the background-limited-noise case. It may be noted that although M 2 assumes the applicability of D* with its A'/' dependence as a valid criterion, the time constant also depends upon A [Eq. (42)]; hence the confusion about area is largely unimportant when using M , . This particular figure of merit is strongly recommended for comparing thermopile detectors. It is dimensionless and it most closely describes the properties of importance to a system designer, who must always consider responsivity, area, noise, and response time. 14. PROFILE
Another parameter of importance to a thermal detector is its profile. This is intimately related to effective area and, as such, must be considered in some detail before any of the criteria suggested above can be used. The response of each couple constituting the thermopile may in some cases be clearly evident in a profile scan.29 Even with thermopiles having a discrete isothermal collector, as shown schematically in Fig. 10, the responsivity is usually not constant over the entire area, particularly at or beyond the chopping frequency corresponding to 0.707 response. Ideally, of course, the responsivity profile should be flat, and fall off abruptly in a manner defined only by the scanning spot size beyond the sensitive area. Similarly, there should be an absence of sensitivity at the cold junctions, since this would contribute a signal of negative polarity to that obtained at the sensitive or "hot" junctions. 15. SPECTRAL RESPONSE
Thermopiles with blackened receivers are usually considered as ideal black receivers far into the infrared. This situation has been abetted by the difficulty of securing standard black receivers for reference measurements in the region of 20-40 p. There now exist good reference^,^' and it is possible 29 30
R. Stair. W. E. Schneider, W. R. Waters, and J. K. Jackson, Appl. Opt 4, 703 (1965). W. L. Eisenrnan, R. L. Bates, and J. D. Merrian, J . Opt. SOC.Am. 53, 729 (1965).
7. RADIATION THERMOPILES
303
to know accurately the spectral response of thermal detectors. Using such a reference detector with well-known properties to approximately 40 p, Bettsj observed a severe decline in the spectral responsivity of thermopiles at wavelengths beyond about 10 p. Thermopiles with blacks of platinum, gold, zinc, and carbon were tested. Measurements of thermopiles relative to a Golay cell were made in the range 1-35 p by Astheimer and Weiner3’ and a small drop in the response, to about 75% of peak value, was observed by them. The author has also observed such a sag in responsivity of the evaporated, thin film thermopiles between 10 and 20 p. To date the cause of this drop has not been determined.
FIG.6. Twelve junction linear thermopile and mount for laboratory radiometric measurement (photo courtesy the Eppley Laboratories, Newport, Rhode Island). 31
D. B. Betts, J . Sci. Instr. 42, 243 (1965).
’’ R. W. Astheimer and S. Weiner, Appl. Opt. 3,493 (1964).
304
NORMAN B. STEVENS
Comparisons of a 2-mm-diameter thermopile with a Gday cell have been ~ ~ a not unexpected decline in thermopile responmade to 3 5 0 in~ which sivity was observed. In this case the relative detectivity was five times greater than that of the Golay cell to 85 p, after which it decayed to comparable performance at 280 p, and to half value at 330 p.
1V. Properties of Thermopile Radiation Detectors It will now be of interest to turn to a comparison of the properties of the bulk, fabricated devices and the evaporated units which usually have a high density of couples in the available space.
FIG. 7. Wire-wound thermopile and mount for high radiant flux density measurements(photo courtcsy the Eppley Laboratories, Newport, Rhode Island).
’’0. Stafsudd and N. Stevens, Thermopile Performance in the Far Infrared, Appl. Opr. 7,2320 (1968).
7. RADIATION THERMOPILES
305
16. BULKMATERIAL DEVICES These devices are made with wires for the active elements, typically silver and bismuth, manganese and constantin, or copper and constantin. Figure 6b shows a mounting that has proved to be very useful in laboratory applications. Figure 6a shows the arrangement of the wires and blackened collector array that constitutes the rectangular receiving area. The rectangular configuration is useful in spectroscopic applications. The cold junctions are provided with thermal mass equal to that of the hot junctions to minimize the effect of temperature drift of the instrument. The “cold” areas are shielded from the incoming radiation. A circular configuration is also available. The devices exhibit impedances of 2-50 ohms, response times (l/e value) of 0.1-2 sec, and sensitivity up to 0.25 pV/pW cm2. A new fabrication technique for bulk material thermopiles is illustrated schematically in Fig. 7. Here the active materials are wrapped around a rectangular support and appropriate blacking is applied on the junction
FIG.8. Thermocouple assembly for spectroscopic instruments (photo courtesy Perkin-Elmer Corporation, Norwalk, Connecticut).
306
NORMAN B. STEVENS
surface, facing the radiation. This design permits the fabrication of large area thermopiles, up to 1 in. square, with sensitivities typically 0.1 V/W cm2. Also shown in Fig. 7 is a typical mounting package. Another mounting for a rectangular (2mm x 0.2mm) thermopile is shown in Fig. 8. This device, which is particularly well known to spectroscopists, is an integral part of a spectrometer. The post which holds the
FIG. 9. Thermopiles as reference detectors in spectroscopic systems require a variety of optical and physical mountings (photo courtesy Charles M. Reeder & Co., Inc., Detroit, Michigan).
7. RADIATION THERMOPILES
307
thermocouple at its terminus offers little obstruction in the optical system. This thermocouple has the following properties : Responsivity 3-6 V/W (at 13 Hz) 20 msec Time constant Resistance 10-12 ohms Minimum detectable power (1.5-0.75) x lO-'OW Target Gold-blacked gold leaf. Some other mountings of spectroscope thermocouples are shown in Fig. 9. A large number of sensitive areas are manufactured, including 0.5 x 1.5 mm, 1 x 3 mm, 6.0 x 6.0 mm, and 10.0 x 1.0 mm, to cite several examples. All are carefully adapted optically and electrically to the system requirements for which they are designed.
17. THINFILMDEVICES Advances in vacuum deposition techniques and improvements in photolithography have facilitated the fabrication of thin film thermopiles. The practical result is that very small devices can be made with a density of 20 or more couples per millimeter, a density far exceeding that achieved with bulk material. This permits much greater design flexibility with respect to responsivity, time constant, and impedance. Referring again to the thermopile schematic shown in Fig. 5, it will be noted that two materials are used, with the darker pattern being deposited first. This is accomplished in a vacuum evaporator chamber which is provided with a source of the desired material. Usually, thermal heating of the material in a metal boat, or electron beam heating of the material is used to provide a stream of atoms of the material, e.g., antimony or bismuth. This material is constrained to the pattern illustrated in Fig. 5 by positioning over the substrate and membrane a mask which is provided with openings where material deposition is desired, The mask is prepared by photoetch techniques from a master typically 50 times larger. This reduction to the mask dimensions permits one to obtain bar widths W of in., placed in proper position with corresponding accuracy. To produce the composite evaporation shown in Fig. 5, the mask may be rotated (or a second mask used) and the second material is evaporated. Clearly, evaporation orders, rates, and general procedures are critical aspects of the technology. The precision of photolithography allows the use of repetitive patterns in thermopile fabrication. This capability greatly reduces the complication usually inherent in detector array fabrication in which repetitive procedures must be employed. Clearly, all thermopiles of an array must perform
308
NORMAN B. STEVENS
BLACKENING
RADIATION E M I T T E D
THERMOELECTRIC MATERIAL N O . l
THERMAL AND ELECTRICAL CONDUCTOR THERMOELECTRIC MATERIAL N 0 . 2
SUPPORTING FILM
FIG.10. Schematic of thermocouple with isothermal collector
similarly, but the important point is that the replication so readily attained with photoetch techniques obviates the need for multiple fabrication steps in making the array. Some interesting thermopile arrays will be shown in the following section. The active materials generally used in making evaporated thermopiles are antimony and bismuth. These evaporate readily and have a high figure of merit.34 The use of alloys is a promising avenue for securing better devices with respect to responsivity alone. However, the difficulty of maintaining a given composition throughout the period of the deposition has delayed the appearance of evaporated alloy thermopiles. Recent developments with electron beam evaporation and sputtering will ease this difficulty and some improved, evaporable alloy materials can be expected to be used in thermopile fabrication. A problem of the thin film thermopile not generally shared by the bulk material devices is flatness or uniformity of profile. This refers to the absence of responsivity peaks and valleys as a small scanning spot is used to explore the receiver or sensitive area of the device. In the case of bulk devices the collector area is thermally massive, with high diffusivity. This condition is not as readily satisfied with an evaporated device. A technique to minimize the unwanted variations in responsivity over the sensitive area is to provide a third material of high thermal diffusivity distributed throughout the sensitive area. The third material is arranged to leave the electrical circuit of the thermopile virtually unaltered and to be of such thickness and thermal conductivity as to permit temperature 34
See Smith rt al.,' p. 78; L. Geiling. Ann. Telecornm. 5,417 (1950).
7. RADIATION THERMOPILES
309
COLLECTOR PATTERN (IMM x 1 MM)
t
t
t
9
A
X-
19
$ s s z RELATIVE RESPONSE
APPROX M A T E SCANNING SPOT S I Z E
u
-
‘*o
SPOT P O S I T I O N , X
FIG.!1. Responsivity profile of thermopile with isothermal collector.
equalization throughout the sensitive area in a time small compared to the device time constant. Thus, it may be considered an isothermal collector. Figure 10 shows one possible arrangement for the isothermal collector, in which it is simply placed in series with the “hot” junction.35 The resulting profile (Fig. 11) shows an absence of responsivity positional structure at scanning frequencies below that corresponding to the device time constant. A typical evaporated thermopile with a sensitive region 1 mm square is shown in Fig. 12. The antimony (Sb) and bismuth (Bi) active elements are evaporated through photoetched masks to provide 15 couples in series. The output leads may be contacted by welding or by a conductive epoxy. The entire device is based on a round sapphire substrate with a groove (as shown) or a circular hole over which is mounted the supporting membrane. The diffusivity and thermal mass of the membrane are small compared to other thermal losses in the structure. The properties of this 1 mm square thermopile and other representative devices, as shown in Table I, point up the major responsivity and impedance 35
See Smith, et ul.,’ p. 86
310
NORMAN B. STEVENS
FIG.12. I mm x 1 mm thermopile with fifteen couples (photo courtesy Santa Barbara Research Center, Goleta, California).
differences between bulk material thermopiles and evaporated thin film devices. Figures 13-15 are illustrations of the other evaporated thermopiles described in Table I. These serve to illustrate the diverse geometries of modern evaporated thermopiles. The 0.25 rnm square thermopile shown in Fig. 13 has been subjected to extensive environmental testing. Throughout temperature changes from 80 to
TABLE I CHARACTERISTICS OF EVAPORATED THERMOPILES Characteristic
1 x I mm (Fig. 12)
0.25 mm x 0.25 mm 2 mm diameter 0.12 mm x 0.12 mm (Fig. 13) (Fig. 14) (Fig. 15)
9, responsivity (vacuum) (V/W) time constant (vacuum) (psec) Z, impedance (K-ohms) NEP (W) D* (cm Hz''~/W)
50
220
160
280
100
75
150
13
T,
M2
6.3 2.1 x 5.0 x 10' 0.10
10 5.9 x lo-" 4.2 x los 0.09
47 1.7 x lo-'' 1.0 x 109 0.15
5 3.3 x 10-" 3.6 109 0.19
FIG.13. 0.25 mm x 0.25 mm thermopile with five junctions (photo courtesy Santa Barbara Research Center, Goleta, California).
312
NORMAN B. STEVENS
FIG.14.2.0mm diameter thermopile with 89 couples (photo courtesy Santa Barbara Research Center, Goleta, California).
400”K the responsivity, time constant, and impedance of this device were measured. These parameters all were found to increase with decreasing temperature. The units survived shock and vibration in all axes as follows : sinusoidal to 40 g at 250-2000 Hz; multiple shocks at 250 g for a duration of 0.7 msec. 18. EVAPORATED THERMOPILE ARRAYS
Figure 16 is an interesting array of thermocouple junctions which provides for detection of the centering of a thermal image. The staggered black areas are underlain by “hot” junctions of reversed polarity. Such a device is useful as the detector of a horizon sensor. An array of eight thermopiles is shown in Fig. 17. Here each 0.4mm x 6.0 rnm thermopile contains 40 junctions connected in series. The external connections between the various thermopiles are readily made by the use of evaporations through photoetch masks.
7. RADIATION THERMOPfLES
313
FIG. 15. 0.12mm x 0.12mm thermopile with five couples (photo courtesy Santa Barbara Research Center, Goleta, California).
A more complex thermopile array is the linear arrangement of 45 thermopiles, each containing 11 couples, shown in Fig. 18. One common lead and 45 separate electrical connections have been provided. These arrays are fabricated on a solid backed substrate and exhibit excellent resistance to both mechanical and thermal A typical spectral coverage of these detectors is shown in Fig. 19. 36
R. W. Astheimer and S. Weiner, Appl. Opt. 3, 500 (1964).
314
NORMAN R. STEVENS
FIG.16. Two 20-element edge detectors on a single substrate (photo courtesy Barnes Engineering Co., Stamford, Connecticut).
7. RADIATION THERMOPILES
315
FIG. 17. Eight thermopile arrays. Each 0.4 mm x 6.0 mm thermopile contains 40 junctions (photo courtesy Barnes Engineering Co., Stamford, Connecticut).
316 NORMAN 9. STEVENS
FIG. 18. Forty-five thermopile arrays of 0.75mm x 3 . 9 m detectors, each with eleven junctions (photo courtesy Barnes Engineering Co., Stamford, Connecticut).
7. RADIATION THERMOPILES
317
WAVELENGTH-MICRONS
FIG. 19. Spectral response of typical thermopile, showing excellent and uniform sensitivity to radiation over a wide band of wavelengths (courtesy Barnes Engineering Co., Stamford, Connecticut).
V. Conclusion
Much recent development has produced thermopile radiation detectors that are sensitive, stable, inherently rugged, and responsive to radiation over a wide range of wavelengths. These properties are realized without cooling and without any electrical bias. Their inability to respond well in submillisecond time is a disadvantage for some systems applications. However, where the information rate is in the domain of greater than one millisecond, where cooling may be a problem, or where wide spectral bandwidth is needed the thermopile detector should definitely be considered.
ACKNOWLEDGMENTS The author wishes to thank L. H. DeVaux and D. D. Errett for many helpful discussions and suggestions. I wish also to thank D. E. Bode for his technical advice during the thermal detector development.
LISTOF a
ll
T V
r E 1
SYMBOLS
Seebeck coefficient or thermoelectric power (V/"C) Peltier coefficient, rate of heat exchange per unit of electrical current absolute temperature ("K) emf(V) Thomson coefficient, rate of heat evolution per unit electrical current, and per unit temperature gradient thermoelectric force, thermal emf (V) length of thermocouple arm
318
Q K
NORMAN B. STEVENS
rate of heat transfer or evolution specific thermal conductivity electrical current electrical resistance area of thermocouple arm thermal conductance electrical specific resistance electrical conductivity thermal resistancc responsivity (V/W) Lorentz number figure of merit, materials specific heat thermal capacitance radiant power, watts height of sensitive area width of sensitive area evaporation thickness device time constant number of hot junctions
Heterodyne Detection and Other Special Techniques
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CHAPTER 8
Low-Level Coherent and Incoherent Detection in the Infrared R.J . Keyes and T. M . Quisl I . INTRODUCTION .
. . . . . . . . . . . . . . .
11. LOW-LEVEL INCOHERENTDETECTION. . . . . 1 . Our Environmental Radiation and BLIP Detection. 2. Signai and Noise Currents in Photoconductors . , 3 . Minimum Detectable Power in Terms of D1* . .
. . . . . .
32 1 322 322 328 332 336 345 345
. .
350
. . . . . . . . . . . . , . . .
.
.
4 . Copper-Doped Germanium . . . . . . . . . . 111. LOW-LEVELCOHERENT RADIATIONDETECTION . . . . . 5 . Heterodyne Detection and Frequency Response. . . . . 6. Ge:Cu as a Theoretically Perfect Coherent Detector at GHz Frequencies . . . . . . . . . . . . . . I . Discussion . . . . . . . . . . . . . . . APPENDIX . . . . . . . . . . . . . . . .
.
.
. . 353 . .
355
I. Introduction Sensors are now available for the detection of faint coherent and incoherent signals in the infrared region of the spectrum extending from the 1 to 30 p. For the first time the theoretical limits of detection imposed by photon noise are a reality rather than a hypothetical boundary that could only be approached at very high photon noise levels. The barrier to the lower limit of signal detection has switched from the sensor to the environment into which it must operate. It is the intent of this chapter to present those detector and environment parameters which are of first-order importance to the small signal detection problem. A complete treatment of low-level detection, even in the restricted portion of the spectrum dealt with here, should include the vast area of science and technology ranging from quantum mechanics to Dewar design. However, the general tenor of this text lies somewhere between theoretical and pragmatic, reflecting perhaps to a large extent the authors’ experience in the field of infrared detection. It is hoped that the references and other chapters in this volume will help supplement obvious deficiencies.
321
322
K. J. KEYES A N D T. M. QUBT
In practice, one can often utilize the same sensing element to measure both coherent and incoherent signals. In fact, copper-doped germanium photoconductors ideally perform both functions, and for that reason many details concerning preparation, physical properties, and fabrication of such detectors are presented. Although the sensors-the nucleus of both types of low level detection systems-have much in common, the peripheral problems germane to each system are quite different. These differences were felt to be of sufficient importance that each mode of detection (coherent and incoherent) is treated separately in Parts I1 and 111. This separation introduces unavoidable redundancy, for which the authors apologize. 11. Low-Level Incoherent Detection 1. OUR ENVIRONMENTAL RADIATION AND BLIP DETECTION
Because the human eye does not see infrared radiation, one is often not cognizant of the vast quantity of radiation emitted by all the objects of our environment. Every substance (not at absolute zero) emits radiation flux that very closely obeys the well-known Planck equation multiplied by an emissivity factor
whcre Wi is the radiant flux emitted per unit area per unit increment of wavelength (W/cm2/cm AA) of a blackbody of temperature Tand emissivity c ; Wc1n2, and and C, and C 2 are constants, C , = 2 7 ~ ~ 1 13.74 x C, = hc/k zz 1.44 cm O K . The peak in the spectral distribution is accurately described by the Wicn displacement law :
R,
=
a/T,
(2)
with u = 2897.9 p deg, and the total flux radiated per unit area by the surfxctce over all wavelengths is expressed quite simply by the StefanBoltzmann law :
w=
037.4,
(3)
where c = 5.7 x W cm * "K is the Stefan Boltzmann constant. These equations are basic to the calculation of detector performance in the infrared region.a A plot of the Planck distribution for the critical 300°K temperature of our surroundings is shown in Fig. 1 . It is obvious that nearly "Calculations to a first approximation can be handled nicely with the aid of a GE Radiation Calculator 0 1 Autonctics Photon Calculator.
8. LOW-LEVEL
COHERENT/INCOHERENT DETECTlON IN THE INFRARED
323
32t
x
(P)
FIG. 1. Radiant emittance of a 300°K blackbody with the 8-12p atmospheric window indicated.
the entire emission occurs within the I-3Op region. To establish a bench mark for the power densities involved in blackbody emission compared to the more familiar visible emissions of our environment, Fig. 2 is presented. I t may be surprising to note that a 300°K blackbody radiates about six times more power per unit area than is reflected by a white sandy beach on a clear summer day in the visible portion of the spectrum. Even the air we breathe radiates, If we could see in the infrared, the atmospheric emission would produce a sensation analogous to that observed within a sunlit cloud in the visible region : light emanating from all directions. This is the hostile environment in which an infrared sensor must function. It hinders the capacity to detect weak signals by introducing two distinctly different forms of noise. One type of noise stems from the fact that either the emissivity or the temperature of the undesired, but ever-present, background may not be constant in either the space or the time domains. Usually, these variations
324
R. J. KEYES AND T. M. QUIST
Temperature of blackbody
(OK)
FIG.2. Radiant emittance (W/cmZ)as a function of blackbody temperature. Radiances of familiar scenes in the visible region are indicated for comparison.
are only unique to a particular situation and hence are not amenable to a general mathematical formulation. An example of this type of fluctuation is found in atmospheric infrared absorption. Cells of air, because of temperature, pressure, or composition changes in both the spatial and time domains, introduce false signals into a detection system. Usually, these variations display a l/f temporal spectrum which can be effectively discriminated from true signals by frequency selection in electronic circuits.
8. LOW-LEVEL
COHERENT/INCOHERENT DETECTION IN THE INFRARED
325
Space-filtering techniques’ are quite effective in reducing undesirable spatial inhomogeneitiesto a tolerable level. Although these effects are treated lightly here, it requires great effort to eliminate them in practice, and the cure becomes especially difficult in the 5-3Op region when the signal is faint. The atmospheric variations are large at low altitudes and the usual techniques involving moving retical choppers are harassed by the annoying fact that the chopper itself becomes a source of undesirable emission. Nonetheless, solutions to these problems can be found, and this effect is not considered henceforth in this chapter. The second source of noise resulting from background radiation is often called “photon noise.” It establishes the absolute lower limit of detection of any radiation sensor when all other noise sources have been eliminated in comparison to it. The genesis of photon noise lies in the fluctuation phenomenon of a Bose-Einstein ensemble of radiators. The theory of the fluctuations in steady streams of thermal radiation was first presented by Lewis2 The formulation of photon noise can be carried out in a variety of ways depending on one’s purpose, and a number of elegant methods are presented by Jones.3 If pb, an average power level of background photons,3aimpinges on a detector, the mean-square fluctuation of incident photon flux per unit of time is
where hv is the photon energy and is the temperature of the background source. The [l - exp( - hv/kT,)] term is a consequence of the Bose-Einstein nature of thermal radiators. For detectors which have a long-wavelength cutoff such that hv b kTb the effective radiation fluctuations approach a Poisson distribution, and for all practical purposes [l - exp(-hv/k&)] z 1. Unless specifically stated we shall assume this approximation to be valid in the remainder of the text. A perfect sensor, which yields a single unit of charge flow per incident photon, requires an incident signal power =
(2pbhVB)”2
(5)
in order to produce an rms voltage equal to the photon noise generated by the background flux in an electrical bandwidth B. If due to reflection losses,
’ J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, and R. G. Richards, “Infrared Physics and Engineering.” McGraw-Hill, New York, 1963. W. B. Lewis, Proc. Phys. Soc. (London) 59, 34 (1947). R. C. Jones, Advanc. Electron. 5, 1-96 (1953). ”The background photons include those of the signal as well. For most situations the contribution from the signal is small, but in special situations they must be considered.
326
R. J . KEYES AND T. M. QUIST
transparency, or a noneffective absorption process only a fraction q of the incident photons produces free carriers, Eq. ( 5 ) becomes ps = ( 2 F b y )
(generation noise)
where 11 is the quantum efficiency of the sensor. Photodiodes in which each photon-induced carrier is swept across a p-n junction or a vacuum can be in this category provided all other sources of noise are eliminated. Photoconductors, however, can never achieve the “photon noise” limit, because of the added recombination noise, which is of the same magnitude as photon noise. Recombination noise has its basis in the statistical fluctuation4 in the rate at which photogenerated carriers recombine from an excited to an initial state. The rms signal power required to produce a SIN = 1 in the photoconductive case is
9, = ) ; j2
F,,hvB ‘I2
Scnsars which have a minimum detectable power expressed by Eq. (7) are sometimes referred to as BLIP5 detectors (background limited infrared photoconductor). A rather special case of BLfP operation occurs when the fluctuation in the signal photon stream is the dominant source of noise. For this condition the minimum detectable rms power becomes
P, = 4hvB/q. (8) As will be shown later, this is only a factor of two greater than the minimum detectable power for a perfect heterodyne receiver. Physically, Eq. (8) states that one has a 50% probability of detecting a signal when there are two absorbed photons per measuring time interval. For conditions of BLIP operation the minimum detectable signal is determined by both the magnitude and wavelength of the background flux impinging on the sensor, N6ise equivalent power (NEP) has been widely used as a general figure of merit for weak signal detection. Specifically, it is the amount of incident signal power which will produce an rms response (voltage or current) equal to the rms noise of the detector for a given band pass. Figure 3 shows the NEP of a BLIP detector at 14 p as a function of the conical angular field of view H of the sensor into a unit emissivity background at temperatures of 100 and 300°K. Sets of curves are drawn for the two situations where the maximum wavelength response is 14 and 30 p. K. M. van Vliet, Proc. I.R.E. 46,1004 (1958).
’ See Jamieson et a/.’
8, LOW-LEVEL COHWENT/INCOHERENT DETECTION IN THE INFRARED 327 I0’”I
16”-
-12-
10
10’~-
-
-3 -a
-15-
z 10
1CP-
tot7-
Field of view ( r a d )
FIG.3. The minimum NEP as a function of detector field of view (0 rad) for 300 and 100°K background temperatures. Sets of curves are drawn for two values of detector maximum wavelength response: 1, = 30 and 14 p.
The lower limit of NEP under theoretically perfect conditions is determined by the fluctuations induced by the signal flux as expressed by Eq. (8) when 13 + 0. However, when one considers problems of signal detection within our atmosphere, values of 8 less than lO-’rad are somewhat academic. Collection mirrors which are diffraction limited to rad at 14 p are large (greater than 1.7 m in diameter) and expensive. Even if they are available, the distortions introduced by atmospheric inhomogeneities produce
328
R. I. KEYES AND T. M. QUlST
“dance”6 in target images in excess of rad, which forces the observer to dilate the field of view to ensure that the signal will remain on the detector. In addition to being exposed to the external background radiation, a detector sees the infrared radiation emanating from the cavity in which it is enclosed. For those circumstances where the enclosure temperature is relatively high and the external field of view is small, the NEP may be dominated by the photon noise induced by the cavity blackbody emission. For example, a detector which has a long-wave cutoff of 14 p and an area of 1 cm’ can never achieve an NEP of better than 8.4 x W for a 1 Hz bandwidth when it is surrounded by a cavity at liquid nitrogen temperature. The perfection of sensors toward the ultimate limit is a process of diminishing the excess sources of noise within the detector and its amplifying circuits. These sources of noise are in most instances definable in terms of known parameters. The detailed analysis of these parameters is important to the selection of possible photoconductive materials for low level detection. 2. SIGNALAND NOISE CURRENTS IN PHOTOCONDUCTORS The path to low-signal detection is the process of elimination of all noise currents with respect to the signal. We shall present the mathematical expressions for the pertinent sources of noise and derive an expression of noise equivalent power in terms of D1*which is quite general for all types of photoconductors. The detailed calculations of thermal generationrecombination (g-r) noise, which are very sensitive to the photoconductor parameters, is given in the appendix, but the results are incorporated in the graphs of this section. In photoconductors the total mean-square noise current ’,i can be expressed as a sum of the individual mean-square noise currents, i,2
iI2
+ i22 + i3’ +
+ ’,i
(9) and the desired result is that the square of the rms signal current ( i s 2 ) exceed this sum, i,Z > i n 2 . (10) We shall in our treatment consider only the nearly perfect photoconductors which are void of those noise currents, such as l/f, which have their origin in either contact imperfections, surface, or trapping mechanisms. The noise currents considered are : (1) in,,, the generation-recombination noise induced by the signal flux, (2) i, the generation-recombination noise induced by the background flux in the field of view, (3) i, the generation-recombination noise induced by the photon flux emanating from the detector cavity walls, =
G. N. Plass and H. Yates, in “Handbook of Military Infrared Technology” (W. Wolfe, ed.), Chap. 6, Section 6.6. Office of Naval Res., Washington, D.C., 1965.
8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 329 (4) i,-,, the thermal generation-recombination noise due to the finite temperature of the detector, governed by Boltzmann statistics and the laws of detailed balance, and ( 5 ) it,,, the effective Johnson noise of the sensor and load resistor-amplifier assembly. Four of the five noise currents listed above are the consequence of the statistical fluctuations in the rate of generation and subsequent recombination of free carriers in photoconductors. Individually, each of these currents can be expressed as follows : a. Signal Noise
i& = 4G2e2P,q1B/hc, (11) where e is the charge on the electron, P, is the power in the signal beam of photon energy hc/A, and q is the quantum efficiency of the excitation process ; G is the photoconductive gain, which will be discussed in more detail later. The factor of four would be reduced to two if only generation noise were present. b. Background Noise ib2 = 4G2e2Aii2yA[sin(8/2)]213, (12) where An2 is the mean-square number of photons emitted per unit area by a blackbody in the spectral region to which the detector is sensitive. The [sin(8/2)] term expresses the fractional portion of the background radiation seen by the sensor of area A through a full cone angle 6 (see Fig. 4). From Planck’s law Limperis’ derives the approximate value of Aii2 in terms of the background temperature and maximum wavelength response 1, as :
where hc/;l, kTb, a condition which is applicable to our considerations. We shall make the additional simplification of retaining only the last term within the bracket, 1/AC2. Combining equations, we obtain ib2 =
8G’e’nkTb[ exp hAC2
-
) ( 2”)’
hc q A sinl.,kTb
_ I
B
c. Cavity Noise Using the same approach as that for the background noise, one obtains z,-2
=3
)
j e x p - _hc_ G2e2qAB, A& T,a,
since the cavity at T,,, very nearly surrounds the detector, the sin(B/2) % 1.
’ T. Limperis, in “Handbook of Military Infrared Technology” (W. Wolfe, ed.), Chap. 1 1 . Office of Naval Res., Washington, D.C., 1965.
330
R. J . KEYES AND T. M. QUIST
FIG.4. Detector-cavil y-background configuration.
d. Thermal Generation Recumhination Noise Thc thermal generation-recombination noise current, although quite straightforward, is a complicated relationship between Boltzmann statistics and the parameters which are inherent in the principle of detailed balance of the particular photoconductor at thermal equilibrium. The details of the thermal (g-r) noise current in photoconductors has recently been presented by Long'; a derivation more suitable for our purpose is presented in the appendix. Stating the results of the appendix, we have for a pure intrinsic photoconductor of energy gap E , = hc/R,
where t is the thickness of the material, z is the hole-electron lifetime, and m* refers to the density-of-states mass of the free holes and electrons. HgCdTe and PbSnTe are representative intrinsic photoconductors. For an intrinsic photoconductor which has a donor impurity density that remains ionized at all temperatures of interest, the generationrecombination noise is somewhat modified' and has the form
Here no is the density of low-ionization-energydonor impurities. In impurity photoconductors such as Ge:Cu and Ge:Hg the g-r noise term takes on a slightly different form,
D. Long, Infrared Phys. 7, 121 (1967).
8. LOW-LEVEL
COHERENT/INCOHERENT DETECTION IN THE INFRARED
331
The ionization energy of the acceptor impurity is so chosen that Ei = hc/,?,. The quantities N , and N , refer to the acceptor and donor impurity concentrations, respectively. As usual, T~ represents the lifetime of a photoexcited hole. The effective degeneracy of the acceptor ground state is p, which is 3 for copper in germanium.
e. Johnson Noise qf the Equivulent Load The final noise current to be considered is that due to thermal Johnson” noise in a load resistor and/or the detector. The load resistance is not a unique quantity. Its magnitude is often determined by the value of the detector resistance, which is quite often temperature and background dependent. Normally, one writes the Johnson noise current of a load resistor as i& = (4kTL/RL)B. (17) In order to obtain maximum signal voltage at the input to a preamplifier, it is customary to match the load resistor to the impedance of the photoconductor, which is critically dependent on the material from which it is fabricated and the operating temperature. We shall divide, : i into two components :hi = F(ii-,) (4kTL/RL)B. U8a)
+
The reason for this division is as follows: For low impedance photoconductors the Johnson noise current of the detector or its equivalent load is mathematically similar to its g-r component and can be expressed as a function of i:,. If at low temperatures the impedance of the detector + co, it is unrealistic to consider the thermal noise in an equivalent load. In practice, it has been found, as reported in the section concerning G e : Cu, that the maximum value of commercially available metal film resistors that demonstrate only Johnson noise at low temperatures is in the range of 30meg0hms.~”The introduction of the 4kT‘,B/R, term ensures that the practical value of Johnson noise is always represented in the general treatment when the sample impedance approaches infinity at low temperatures. The F(ii-,) term ensures the proper representation of thermal noise at low detector impedance levels. For intrinsic and impurity photoconductors
J. L. Lawson and G. E. Uhlenbech, “Threshold Signals,” Chap. 4. McGraw-Hill. New York, 1948. ’”Admittedly. values of ideal load resistors in excess of 30 megohms are feasible. The author chose this value to represent the present state of the art. The reader can, if the art improves, utilize values of R , that are appropriate to the existing art.
332
R . J . KEYES AND T. M. QUIST
where p is the mobility of the majority free carriers and I is the distance between electrodes. For extrinsic materials, in which the impurities are all ionized, the expression becomes
At all temperatures of interest the 4kTL/R, term can be omitted. 3. MINIMUMDETECTABLE POWER IN TERMS OF DA* By equating the signal current to the total noise currents we can obtain the signal power required to yield a signal to noise ratio of unit (SIN = 11, namely
9,= (i;)’/’hc/GeAq.
(19)
A figure of merit for the comparison of infrared detectors, DfI, can be expressed as followsgb:
This expression in the mks system thus has the dimension of m Hz”’ W-’ Substituting for in2 the five dominant noise currents, we obtain the complete expression for DXI, for impurity photoconductor (Ge :Hg):
signal
background
cavity
exp -
-)(Z,& k
hc
1
+
)-
thermal g-r
k T , , V W
G2e212
Johnson Idetector)
Johnson (load) ~ - l ) is a widely accepted figure of merit for infrared detectors, it 9bAlthough D,* (cm H Z ” W may be cumbersome to use. Since its units are not consistent, one must exercise caution in the dimensions of the parameters involved in its calculation. With hindsight it seems that if DA* had been defined in units of m Hz”’W- I , a much more sensible and consistent figure of merit would have been obtained, namely, DXI, (m H Z ” ~W-’). We have made our calculations in the latter units: however, in deference to established usage we have plotted our results in terms of DL*.
8. LOW-LEVEL COHERENT/INCOHERENT
DETECTION IN THE INFRARED
Defector Temperature
333
(OK)
FIG.5. Plot of Dt (cm Hz''' W - *) as a function of detector-cavity temperature for PbSnTe (iO'" and 10" cm-3 donor impurities) and Ge:Hg. Also indicated on the graph is the maximum D L as a function of field of view into a 300°K blackbody. The D b limit as a function of cavity temperature is also plotted. A, = 1 4 ~ '
Since the commonly accepted figure of merit Di* has dimensions of cm Hz'l2 W - ', the value obtained from Eq. (21) must be increased by a factor of 100 to conform to the commonly-accepted definition. Theoretical plots of Di* as a function of sensor and of cavity temperature T,,, are given in Fig. 5 for Ge :Hg and PbSnTe when 0 = 0. Curves for two values of impurity content (loll and 10'4cm-3) of PbSnTe are drawn. The value of 10" represents the best purity that can probably ever be obtained, while the concentration of 10'4cm-3 is felt to be representative of the purity obtainable in the near future. Indicated on the right-hand side of each plot is the maximum D,* possible for various fields of view into a unit-emissivity background of 300°K. Also plotted is the limit established by the photons emanating from the cavity walls. For small signals the first term within the bracket of Eq. (21) can be neglected. The photoconductive gain G is expressed in Eq. (22).
334
R. J. KEYES AND T. M. QUIST TABLE 1 Parameter
PbSnTe
Ge:Hg
1.40
1.45 x IO-'" 10 x to x 10-3 1o4
3
x
10-31
10
x
x 10-2 x
I I
x 10
t
1 5 x lo-'
1.4 x 10-5
32
10-.32
2 1.45 x lo-''
lWS
103
10 10 1.45 x lo-'' 1 10-5 10-5 1.4 x 10-5
The values of the photoconductor parameters which were used for the calculations of these graphs are given in Table I. Admittedly, the values of T, p, and t employed for the PbSnTe calculations are optimistically beyond the present state of the art, but because of the infancy of this material compared to the impurity photoconductors, the authors feel that the bias is justifiable. An analysis of D,* equations and graphs leads to some important general conclusions : 1. In uny photoconductive material of the same maximum wavelength cutoff (Ic) the photon induced noise of the signal establishes a minimum detectable power of 4hvB/q. 2. The photon flux from the cavity walls sets another theoretical limit on DA*, but for T,,, < 30°K it is not a contributing factor. At 77°K the maximum D,* possible is 1.2 x 10l3cm Hz'I2 W - ' for & z 14 p, 3. The photon flux reaching the sensor from the thermal radiation in the field of view 0 usually establishes an operational upper limit for D,*. Since background temperatures and emissivities are extremely variable in relationship to a given detection situation, a general analysis is impractical. Typical 0 dependences of Dj,* for background temperatures of 100 and 300°K are indicated in Fig. 3. 4. When the detector and its enclosure are at a very low temperature and the flux from the background is negligible, the major source of noise in both impurity and intrinsic photoconductors is the Johnson noise of the load or
8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 335
the detecting element. In this situation the achievable Dn* is critically dependent on the parameters which regulate the photoconductor gain G. As described by Rose," G is the ratio of the lifetime of an optically-excited carrier to its transit time between electrodes of separation 1. When a photoconductor has ohmic electrodes, which do not inhibit the flow of carriers in and out of the detector, G can be expressed as G =Ep/i, (22) where E is the electric field across the photoconductor, p is the mobility of the excited carrier, and z is the average lifetime of the excited carrier. In photoconductors G can take on values ranging from near zero to above lo3,depending on the parametric values of the material, its dimensions, and the electric field applied. It should be noted, however, that G %- 1 implies that many charged carriers traverse the electrodes for each photon absorbed, and hence for high-gain detection the ohmicity of the contacts becomes very important. Avalanche' gain is an entirely different phenomenon involving impact ionization. A discussion of avalanche multiplication is beyond the scope of this chapter. Let it suffice to say that it is not a useful technique of gain in impurity or one free-carrier photoconductors. It may be very advantageous, however, in intrinsic or two-carrier materials. For impurity photoconductors when thermal noise of the load resistor (3 x lo7 ohms) dominates Da* K GI, and the maximum achievable D,* is obtained when the Epz product is the largest. Only the lifetime in a specific material is amenable to appreciable control. As explained in the section on copper-doped germanium, large values of z are obtained through the elimination of residual donor impurities in the host crystal. 5. Because the absorption coefficient for pair producing radiation in PbSnTe is large (> lo4 cm- '), a reduction of sample thickness to the micron range is effective in increasing DA* when thermal noise predominates. Not only does a decrease of t reduce the total number of thermally generated carriers which introduce noise, but it also raises the sample resistance, which in turn permits larger electric fields to be applied to the detector without undue 12R heating. 6. If the mixed crystals could be deposited in thin layers ( 1 p) of high purity and mobility, Da* performance comparable t o that of the impurity photoconductors would be possible at slightly higher temperatures. A general advantage of intrinsic over impurity photoconductors is their ability to maintain higher Dn* at comparatively elevated temperatures. Although the introduction of low ionization energy impurities into intrinsic materials reduces the maximum Dn* at low temperatures, it extends the N
'' A. Rose, in "Photoconductivity Conference" (Proc.Atlantic City Conf.) (R. G . Breckenridge, ''
B. R. Russell, and E. E. Hahn, eds.), p. 1 1 . Wiley, New York and Chapman & Hall, London, 1956. K. M. Johnson, I E E E Trans. Electron. Devices 12, 55 (1965).
336
R. J . KEYES AND T. M. QUIST
intermediate values of Dn*to a higher temperature. This can be an operationally important factor when D,* is limited by background photon noise and the degree.of cooling is restrictive. As stated previously, for most small signal detection systems the thermal emission of the background in the field of view limits the achievable signalto-noise ratio. Under this condition the designer usually reduces the sensor field of view in order to obtain a more favorable SIN, but he does so at the expense of versatility and acquisition ability of the system. To overcome this lack of versatility an array of sensors might be used. It should be borne in mind that unless the Dn* value of each element in an array or storage tube is comparable to that of a single element device, much of the advantage is lost. For example, if an array or tube has n elements, then each element must have a Dn*value > 1/& times the DA* obtainable from a single element device used in a mechanically scanned mode if the composite structure is to be of advantage in SIN. The larger the number of elements in the array, the less stringent is the requirement on individual performance. For arrays or other devices having lo5 elements, each element has to have a DA* 1/300 of that of a single-element mechanically scanned device in order to obtain comparable performance. From a more optimistic point of view, an array with lo5 perfect elements can detect signals 300 times weaker than a perfect single element used in a scan mode. To this point we have been mainly concerned with the quasitheoretical aspects of low-level incoherent signal detection in the infrared region ; the remaining portion of Part I1 will be more pragmatic, in that it will deal with the actual methods of fabrication and measurement of high-D,* copper-doped germanium detectors for the 1-30 p spectral range. As stated previously, Ge :Cu is not a unique impurity photoconductor, but its problems and performance are representative of those that might be encountered in a host of possible detector materials, of which Ge :Hg, Ge:In, Si :In, Si :A1 are only a few. The authors have selected Ge:Cu as an example because it is the material which they have studied to the greatest extent. An analysis of an intrinsic detector (PbSnTe) is given by Melngailis and Harman in Chapter 4. 4. COPPER-DOPED GERMANIUM
The impurity-photoconductive aspects of Ge :Cu were first reported by Burstein er a/. in 1954.” In the early days of transistor and diode technology this impurity, because of its rapid diffusion and detrimental effect on free carricr lifetime, was considered a tenacious contaminant in semiconductor materials and devices. For infrared detector fabrication the rapid diffusion
‘’ F. Burstein, J. W. Davisson, E. E. Bell, W. J. Turner, and H. Lipson, Phys. Rev. 93,65(1954).
8, LOW-LEVEL
COHERENT~INCOHERENT DETECTIONIN THE INFRARED
337
of copper plus the three acceptor levels associated with each atom permit one to make versatile sensors of different characteristics with a minimum of equipment. Before pursuing the details of infrared detector fabrication and measurements a brief description of the impurity levels of Cu in germanium is in order. Copper introduces three acceptor levels13 in the forbidden band of germanium, one each at 0.04 eV and 0.32 eV above the valence band and one 0.26 eV below the conduction band. Thus, the substitutional copper atom first accepts one, then a second, and lastly a third electron as the Fermi level is increased. It is the 0.04eV level that is of interest when Ge:Cu material is used as a long-wavelength sensor at near liquid helium temperatures. Figure 6 is a schematic band diagram of the copper impurity in germanium. In addition to the copper atoms, other donor or acceptor impurities are present, either as residual or intentionally introduced dopants. For our presentation acceptor atoms other than copper are not considered, but attention is given to donor impurities such as arsenic and antimony which play a vital role in the total photoconductive process. The photoconductive process proceeds as follows : If the temperature of the crystal is below 15"K,thermal excitation of electrons into the copper levels is negligible and all of the copper atoms remain unionized except those that have accepted an electron from a donor impurity atom, in which case the copper atom takes on a net negative charge Cu-. An infrared photon of energy greater than 0.04 eV, upon entering the crystal lattice may excite an electron from the valence band into a Cuo site, producing an additional Cu- level and leaving behind a free hole in the valence band which can move through the lattice by diffusion or under the force exerted by an externally applied electric field. As long as the photon excited hole "lives" photoconduction will persist. Ultimately, the free hole will recombine with an electron from a Cu- site. It is evident from this mechanism that the average lifetime of the hole is inversely proportional to the number of Cuatoms, and is directly related to the density of donor impurities. One can readily see that NDplays a vital role in the photoconductive lifetime zP and hence in the photoconductivity. It is desirable for many applications to make zP as long as possible, which requires ND to be kept very small. Most high sensitivity detectors are obtained from very pure host crystals where ND is the residual impurity remaining in the lattice after maximum purification has been attained. Residual impurity densities in germanium below a concentration of 10'2cm-3 are difficult to achieve. As will be discussed later in the use of Ge :Cu for heterodyne detection, donors are intentionally introduced in order to reduce the lifetime for high frequency operation. In I3
H. H. Woodbury and W. W. Tyler, Phys. Rev. 105,84 (1957).
338
R. J . KEYES AND T. M . QUIST
Conduction band
N,
cu--
cu-
____
~
0 01
O+
O+
O+
0.26
___ 0.32
-
*
0- 0-
*-\
0
! I
I
cuo
-0.04o
o
o
I
c;
-
‘i‘\ I I
o o o
0
0
0
‘I
$;I
I $i-..:’.
/
0
0
0
I & vI
b
E
.
4
Excitation
Recombination Valence band
FIG.6. Energy level diagram of G e at 4°K containing residual donor atoms and showing the triple ionization energies of the Cu atom. The figure illustrates schematically the photoionization of an electron to the 0.04 eV level leaving a free hole and the subsequent recombination of an electron with a free hole in the valcncc band.
view of the impurity photoconductive mechanism of Ge:Cu the first step in the fabrication of detectors is to obtain a very homogeneous germanium host crystal with the desired donor concentration. Many copper-doped germanium detectors have been fabricated from single crystal germanium with a net donor impurity concentration of from ND z 10’’ to 7.4 x 10” atoms/cm3 with a liquid nitrogen temperature mobility p z 4 x lo4 cm2 V - ‘ sec-’ for the purest samples. Prior to indiffusion copper is evaporated or electroplated on to the chemically etched and cleaned surfaces of the germanium wafers. The wafers are then placed inside a quartz tube in a furnace with an 85% argon, 15% hydrogen atmosphere maintained around the sample. The solid solubility of “electrically active” copper in germanium is shown in Fig. 7.13 The maximum
8. LOW-LEVEL COHERENT~NCOHERENTDETECTION IN THE INFRARED 339 TEMPERATURE " C l
I
0.8
~
l
0.9
560
679
838 /
l
l
I0
~
l
I
l
4.1
467 (
l
l
1.2
I
l
l
~
I
\
l
1.3
iOOO/T (OK)
FIG.7. Solid solubility versus diffusion-annealing temperatures for copper in germanium as determined by the density of the 0.04 eV acceptor states. The filled circles represent the data of Fuller et a/. obtained from radiotracer experiments. (The concentration of loi6 cm13 corresponds to an atom fraction of 4.45 x The slope of the solubility curve below the eutectic point is 1.9 eV, while just above this point it is about 1.7 eV. (After Woodbury and Tyler.I3)
solubility of about 2 x 1 O I 6 atoms/cm3 occurs at a temperature of 875°C. The diffusion constant of copper for annealing temperatures in the 700900°C range is fast, about 2.8 x lo-' cm2/sec. This is to be compared to other acceptor impurities in germanium such as gallium and indium, which have diffusion constants in the lo-'' range. The crystals are maintained at the desired temperature for sufficient time to ensure uniform
I
340
R. J. KEY& AND T. M. QWST
distribution of copper, and then removed from the hot furnace and rapidly cooled (usually air quenching is adequate) to freeze in the copper concentration at 8 x 1015atoms/cm3. This is the effective upper limit of usable copper doping due to the occurrence of impurity banding effects at higher concentrations. Material is then lapped from each face to obtain the proper wafer thickness. After the wafers are sawed into 3 mm cubes and chemically etched (CP-4) two indium contacts are soldered to opposite faces of the detector. Care must be exercised when soldering the contacts to keep the temperature low and apply it for as short a period of time as possible in order to prevent the formation of large copper concentration gradients near the contacts due to Cu outdiffusion. The detectors are then cleaned and given a slight chemical etch, one contact is soldered to a copper stud, and a small lead is attached to the other contact. Referring to Fig. 8, we see that the detector when mounted in the Dewar is electrically isolated from the liquid helium heat sink by a sapphire post which is one of the few materials that is a good electrical insulator as well as a good thermal conductor at helium temperature. Electrical isolation of the detector from the Dewar is not necessary, but it allows more versatility in the selection and design of the preamp circuit. The electrical measuring circuit is shown in Fig. 9. A low noise field effect transistor operated as a self-biased source follower is used to transform the high load impedance R , (in some cases 30 megohms) to a more workable
600° C B E SOURCE \
~~
CHOPPER
FIG.8. Physical arrangement for the low background measurement of Cu-Ge photoconductorsat liquid helium temperatures and for the 8-12 p region.
8. LOW-LEVEL COHERENT/INCOHERENTDETECTION IN THE INFRARED 341 LIO He TEMP
LlO N p TEMP
ANALYZER
-
FIG.9. The electrical circuit for the measurement of responsivity and low noise.
value in the kilohm range (15 kilohms). The voltage gain of the source follower circuit is 0.9. The metal film load resistor R, is attached to the helium block to reduce its thermal noise power, while the silicon FET is located on the liquid nitrogen shield to ensure negligible gate current. The dc current through the detector is measured as the voltage across Rc, also located on the helium block. This resistor is located on the helium block for convenience only. Since its resistance is small by comparison to the load resistor, its Johnson noise contribution is negligible even at room temperature. This circuit arrangement permits the measurement of very small noise voltages. For our measurements the limiting noise was the thermal noise of the load resistor R , located at liquid helium temperature. A 600°C blackbody source chopped at various frequencies less than 1OOOHz was used to obtain the detector responsivity. A battery source is used to adjust the bias (positive or negative) of the detector and a high impedance microvoltmeter is employed to measure the voltage across Rc, which is a measure of the dc current through the detector. A low noise preamplifier, used to amplify the output signal from the source follower, is fed to an oscilloscope for measuring the signal voltage and to a wave analyzer which measures the output noise from the detector in a 10-Hz bandwidth, Radiation falling on the detector was limited to the 8-12p wavelength region. Figure 10 is a typical responsivity-electric field (9versus E ) curve for incident radiation in the 8-12p region. The responsivity W is defined as the response per unit of incident radiation. For photoconductors W is usually given in amperes or volts per watt. The responsivity factor used here
342
R. J. KEYES AND T. M. QUIST
c
PI
2 U
5-
0
I00
50
150
E (Volt-cm-‘1
FIG.10. Responsivity versus electric field for the 8-12 /.t region. This curve is symmetrical about the origin, i.e., - E gives the same response as + E. The detector was a 3 mm cube with net donor impurity concentration N D e 7.4 x 10” and Cu concentration of 8 x 1015atoms/cm’.
expresses the detector signal current in amperes (constant detector voltage) as a function of incident power (watts). We feel that the response given as amperes per watt is more closely related to the fundamental photoconductor parameters, namely, W (A/W) = qG(e/hv) = qEpTe/lhv for photoconductors. Within experimental error the responsivity was found to be the same for all values of background and signal intensities measured, and the shape was symmetrical about the origin, i.e., for either polarity of applied voltage. The measured noise equivalent power (NEP) for a 1 Hz bandwidth as a W and about lo-“ W function of background power between 3 x is plotted as a dashed line in Fig. 11. The noise voltage was measured at frequencies of about 300Hz. The theoretical NEP for BLIP detection is the solid line in the same figure; here we have calculated the NEP for BLIP detection to be
NEP
=
~(PJwB/~)”~,
(23)
where Pb is the power incident on the detector, which was deduced from the dc current and the measured responsivity. hv is the average photon energy between 8 and 12 p, B, the electrical bandwidth, is 1 Hz,and q x 0.52 is the quantum efficiency, which includes reflection losses as well as that due to the absorption of the material. The absorption coefficient of 4 cm- for this detector material over the wavelength of interest (8-12 p) was deduced by inserting a 3 mm cube of detector material directly behind the limiting aperture and measuring its transmission at liquid-helium temperature.
8. LOW-LEVEL
COHERENT/INCOHERENT DETECTION IN THE INFRARED
343
P, (Watts)
FIG.11. NEP as a function of background power for the 8- 12 I( region. The solid line is the theoretical limit for BLIP detection and the dashed curve represents the measured values for Cu-Ge.
This absorption coefficient of 4cm-' is in good agreement with that given by Bebb and Chapman,I4 who have reported absorption coefficient data and theory for copper impurity concentrations of 7 x l O I 5 ~ m - A~ com. parison of the experimental and theoretical background-limited curves shows that these detectors exhibit very little extraneous noise for backgrounds as low as about lo-" W or 5 x lo8 photons/sec in the 8-12 p region. Thus any noise contributed by contacts, surface, or other detector parameters is small in comparison to the generation-recombination noise induced by the low background level. This noise equivalent power of 10- W corresponds to an equivalent background temperature of 49"K, but is still about four orders of magnitude above the theoretical minimum detectable signal level of Eq. (8). Extension of noise measurements to lower background levels than shown in Fig. 11 is primarily a problem in decreasing the thermal noise of the load resistor R, or increasing the internal gain of the photoconductor so that the l4
H. B. Bebb and R. A. Chapman, J . Phys. Chum. Solids 28,2087 (1967).
344
R. J. KEYES AND T. M. QUIST
background-induced noise current is dominant. Mathematically, this condition can be expressed in the form ib2 > i&. For the above condition the noise due to the cavity (iza,) and the thermal generation-recombination noise (ii-,) are negligible (KBvnear 4°K). Thus i:h = 4kTLB/R, from Eq. (18b). Multiplying Eq. (23) by the responsivity 2 and squaring gives
Substituting and solving for Pb gives
Pb > kT,hv12/qR,e2E2~Lp2.rp2 as p h + 0. Increasing the load resistance has the additional disadvantage of raising the RC time constant and hence lowering the frequency response of the system. Although it would be desirable to increase the lifetime of the free holes, there seems little hope of significantly raising it beyond the value of 3 x sec which was available in our measurements. At a given temperature below 15°K the hole lifetime can be expressed in terms of the free-hole velocity u p , its capture cross section o p ,and the density of donors N , , i.e.
zp = l/v,a,N,.
(25)
At liquid-helium temperatures T~ z 3 x lO-'sec, corresponding to an ND = 7 x 10" ~ r n - A ~ . significant decrease of N D below this value is beyond present germanium purification techniques. The only parameter of Eq. (22) which is readily adjustable to produce higher gain is the dimension of the detector ( I ) in the direction of the applied electric field. Even with the most advantageous adjustment of the copper doped germanium parameters and load resistance it does not seem plausible that a measured NEP will yield the theoretical minimum of 2hvB. To further investigate responsivity versus temperature, other detectors with higher donor concentrations were checked. Figure 12 is a plot of the normalized photoresponse versus reciprocal temperature for three detectors ~ m - ~ but ), each containing the same copper concentration (-7 x having different donor concentrations (NDNN 7.4 x lo", 1015). AS expected, the relative magnitude of the response is proportional to the reciprocal of the donor densities. There exist two distinctly different slopes for each curve. At low temperatures the slope increases as the donor concentration decreases [slope increases as ( N A - ND)/N,] and when the donor concentration approaches loi5cm-3 the slope approaches zero in this region. For higher temperatures the responsivity increases sharply, as
8. LOW-LEVEL COHERENT~INCOHERENTDETECTION IN THE INFRARED 345 T (OK) 20
15
8
10
0 05
0.10
i/T
7
5
6
0.45
0.20
( O K )
FIG.12. Normalized photoresponse versus l/T for three detectors, each containing the same Cu concentration, but possessing different donor concentrations. The relative magnitude of the response is proportional to the reciprocal of the donor densities.
expected, at about the temperature where thermal generation of free holes begins. The slope of all the curves in this region corresponds to the activation energy of the 0.04 eV copper level. It is felt that the latter increase is due to the increase in z p caused by thermal reemission of the hole captured in an excited state of the neutral copper atom, prior to complete recombination to the ground state. It should be pointed out that responsivity measurements embrace a number of parameters ,up, z p , and u p , all of which can be temperature dependent. Until either the mobility or the lifetime are independently measured as a function of T, one cannot uniquely define the mechanism of the observed responsivity vs temperature data. However, the lack of temperature dependence for highly-compensated crystals is of significance to heterodyne operation, when large amounts of local oscillator power are dissipated in Ge :Cu sensors. The Bat response should permit considerable temperature rise without significantly changing the sensitivity, III. Low-Level Coherent Radiation Detection 5 . HETERODYNE DETECTION
AND
FREQUENCY RESPONSE
The rapid development of single mode, single frequency CO, lasers of high stability and power output has given great impetus to the search for
346
R . J . KEYES AND T. M. QUIST
the ideal heterodyne detector in the middle infrared. The marriage of the COz laser and the heterodyne receiver promises exciting opportunities in the fields of radar,’ communication,’6 and spectro~copy.~’ Heterodyne techniques have been well established in the radio and microwave regions of the electromagnetic spectrum. Over the past decade sensors have been proposed and produced for the optical,’”24 near-IR,2“28 and middle1R29-3’regions, and almost ideal heterodyne receivers using Ge :Cu have been developed for the spectral range of 2-29 p.29In Chapter 9 Teich presents some of lhe more elegant basics of heterodyne detection ; Arams ut al. in Chapter 10 elaborate on the specific problem associated with high frequency operation, and on its application to communications. Again this section approaches the problem of low level coherent detection from a more pragmatic point of view ; emphasizing by example what has been achieved, what the problems are, and what seem to be the greener pastures for the further development of heterodyne devices. By necessity, overlapping areas will be covered by the authors with the certainty that disagreement will result. It is the hope that these differences of opinion will be the most important part of the text. As an appetizer to the main course of heterodyne detectors, it is customary to serve the basic equations which describe the mixing of two parallel electromagnetic waves in the sensor medium. Is
H.A. Bostlck, IEEE J . Quunlum Elwrron. 3, 232 (1967). M. Ross, “Laser Receivers,” pp. 115-118. Wiley, New York, 1966.
K. H. Kingston, Private Communication. A. T. Forrester, J . Opt. Suc. Am. 51, 253 (1961). I ” A E. Sicgman. S E. Harris, and B. J. McMurtry. in “Optical Mascr” (J. Fox, cd.), pp. 5 11-527. Wilcy, New York, 1963. 2 o S. Jacobs, Electronics 36, 29 (1963). 2 1 M . E. Lasscr. Spectrum 3. 73 (1966). 2 2 S. Jacobs and P. Rahinowitz, in “Quantum Electronics 111’’ (P. Grivet and N. Bloembergen, cds.), pp. 481-487. Columbia IJniv. Press, New York, 1963. z3 I,. Mandel. .I. Opt. Soc. Am. 56, 1200 (1966). 2 4 A. E. Siegman, S. E. Harris. and R. .1. McMurtry, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen, eds.), pp. 1651-1658. Columbia Univ. Press, New York, 1964. ” M. I)iIlomenico, Jr.. R. H. Pantell. 0. Svclto, and J . N. Weaver, A p p l . Phys. I d l e r s 1, 77 ( I 962). G . Lucovsky, M. E. Lasser, and R. B. Ernrnons, Proc. I E E E 51, 166 (1963). G. Lucovsky, R. B. Emmons, B. Harned. and J. K. Powers, in ‘Quantum Electronics 111” (P. Grivet and N. Bloembergen, edh.), pp. 1731-1738. Columbia Univ. Press, New York. 1964. ” R. H. Pantell, M. DiIIomenico, Jr., 0. Svelto. and J. N. Weaver, in “Quantum Electronics 111” (P, Grivet and N. Rlnemhergen. eds.), pp, 181 I 1818. Columbia Univ. Press, New York. 1964. 29 M. C. Teich, R. J. Keyes, and R. H. Kingston, Appl. Phys. Letters 9, 357 (1966). 30 C. J. Buczek and C . S. Picus, Appl. Pkys. Letters 11, 125 (1967). F. Arams, E. Sard. B. Peyton, and F. Pace, l E E E J . Quantutn Electron. 3, 484 (1967). I’
’‘ ’’
’’
8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 347 Consider two parallel electromagnetic waves of the same polarization incident on a detector (Fig. 13), a local oscillator wave of frequencyf,, and a signal wave of frequencyf,. If the detector has a linear relationship between response and flux density (photons/sec) of the individual waves, then the two waves will induce a response in the sensor at the difference frequency IfLo - f,l. In theory, the detector can produce outputs at fLo, L , and (fLo + f,), but for all practical purposes, frequencies of these magnitudes are beyond the speed of response of heterodyne receivers. Therefore we shall only consider the difference frequency, which is commonly referred to as the IF frequency in the radio and microwave fields. It has been shown3’ that a perfect heterodyne sensor, which has an average current ,i induced by a local oscillator beam of power P,,, and a corresponding signal current I , induced by a signal power P,, will yield an average current at the difference frequency of the form itF = 2iL0is = [2q2G2e2/(hv)’]PL,P,,
(26)
where q is the external quantum efficiency and G is the gain described in Part 11. It should be noted that in the incoherent detection process the signal current is proportional to the incident signal power ; in heterodyne detection the IF current is proportional to the square root of the signal power. The noise encountered in heterodyne detection is basically the same as that experienced in incoherent systems. Many possible sources of noise exist, but we shall consider only two which are either impossible or tenacious to overcome : (1) generation-recombination noise induced by the local oscillator flux, and (2) the thermal noise associated with the preamplifier loadresistor ensemble. With these restrictions the total mean-squared noise current in terms of measurable parameters can be written as :i
‘
~
PLoB
= 4e2G2q-
:
-
hv
+ -.4kTLB RL
~
-
~
-
FIG.13. Schematic representation of the heterodyne detection circuit. 32
A. E. Siegman, Proc. ZEEE 54, 1350 (1966).
Filters
~
348
R. J. KEYES AND T. M. QUIST
Equation (27) ignores background induced g-r noise because in practice it can always be made much smaller than that introduced by PLo. If it is assumed for thc moment that a nearly perfect amplifier exists and hence the second term on the right of Eq. (27) is small, then by setting i,2 =,:i and solving for P, we obtain the familiar theoretical power detection limit for heterodyne receivers,
Prin= 2hvB/q
photoconductor
(28)
PT"
photoemitter or reverse p-n junction.
(29)
=
hvB/q
At the heterodyne detection limit very small signals are measurable. For example, using a usual bandwidth of 1 Hz and a quantum efficiency of unity the minimum detectable signal (SIN = 1) at 10 p is 2.9 x 10-20W p.c. and 1.45 x 10-" W p.e., which corresponds to one photon per cycle of (IF) bandwidth. It follows from Eq. (28)that the theoretical power detection Iimit improves as the wavelength increases. The results obtained by Teich et on copper-doped germanium are shown in Fig. 14, from which it is obvious that Ge : Cu photoconductors do behave according to theory [Eq. (28)], and yield detectabilities which are much greater than can ever be achieved in the
I0
Ge: Cu DETECTOR '05- HETERODYNE FREQUENCY: 7 0 k H z
a
a ro4-
- 50 - 40
a
%
x
--
-m
U 30 v
a
w Y
20
w
z >-
- 10
0 0
2n
t’. Thus phase retardation is equivalcnt to time displaccment at the detector, allowing for the coherence time to be considered as a parameter. For the heterodyne experiment we may simply write the total electric field operator as a superposition of the operators for the constituent waves.” Therefore the positive-frequency component of the field present at the photodetector, E + ( r ,t ) , may be written E+(r,t ) = All?@,
t,)
+ I,E+(r, t2).
(2) The complcx coefficients A, and 1, contain the relative strengths of the two waves, and are taken to be independent of the properties of the field. The R . J. Glauber, Phys. REU.130, 2529 (1963). R. J. Glauber, in “Quantum Optics and Electronics” (C. deWitt, A. Blandin. and C. CohenTannoudji, eds.), p. 65. Gordon and Breach, New York, 1965. ’’ K.J . Glauber, Phys. Ref).131,2766 (1963). ” S. Jacobs and P. Rabinowitz, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen, eds.), p. 481. Columbia Univ. Press, New York, 1964. M. C. Teich and G. J. Wolga, Phys. Reo. Lefters 16, 625 (1966). 24 25
‘’
9.
COHERENT DETECTION IN THE INFRARED
367
count rate R may therefore be expressed as R = tr{pE-(r, t)E+(r,t ) ) = tr(p[A,*E-(x,)
+ Lz*E-(xz)l
where, as above, the space-time point x t = r, t , is relative to the radiation source. Using the correlation function identityz4 [G"'(x],
xZ)]*
=
G"'(x~, XI),
(4)
this rate may be written in terms of the first-order time-dependent correlation functions @')(ti, t j ) as
R
=
(A1(ZG'l'(t,, t t )
+ (Az\2G'1'(tz,t z ) + 2 Re(Al*3,zG'1'(tl,t z ) ).
(5)
The first two terms on the right represent the intensities which would be contributed by each beam independently of the other; the last term represents the interference. We have assumed that the angular alignment condition required for optimum photomixing is maintained,29so that the angle between the beams is restricted to a value smaller than A/a, where 3, is the radiation wavelength and a is the detector aperture. For this case the correlation function may be taken to vary slowly over the detector, and its spatial dependence suppressed, as above. We could, alternatively, retain the spatial dependence, in which case the condition for first-order coherence discussed in the next paragraph will automatically require the alignment condition to be fulfilled in order to obtain optimum phot0mixing.2~ If the radiation incident on the detector possesses precise first-order coherence, two interesting consequences follow. The first relates to constraints on the correlation functions,30and will provide us with the magnitude of the heterodyne signal. The second concerns the density operator for the radiation field,31and will allow a physical interpretation for the beating process. The condition for maximum fringe contrast, or first-order coherence, has been shown by Titulaer and Glauber3' to be equivalent to the factorization of the correlation function into two complex quantities €(tl) and
W z ): G"'(t1,
t z ) = &*(t,)&(t,).
(6)
With Eq. (3,under conditions of first-order coherence of the total incident radiation field,23we therefore obtain
R
=
IAIIZG(l)(tl,t t )
+ (&1zG'1)(t2,t z ) + 2 Re(ill*d*(tl)i/z&'(t2)}.
'' A. E. Siegman, Appl. Opt. 5, 1588 (1966). 30 31
U. M. Titulaer and R. J. Glauber, Phys. Rev. 140, 3676 (1965). U. M. Titulaer and R. J. Glauber, Phys. Rev. 145, 1041 (1966).
(7)
368
M. C. TEICH
We may also write Eq. (5) in the equivalent form
R
= 1A112G(1)(tl,t l )
+ 11212G(1)(t2,
+ 211111121 IG(”(t1
Y
t2)
t2)l C O S l M l Y t 2 )
+ @S
(8)
9
where q5(tl, t,) is a time-varying function derived from G(’)(tl, t,). The phase angle 8 depends on the geometry of the experiment. While the first-order coherence condition has been used in obtaining Eq. (7), this is not so for the result in Eq. (8). Using the correlation function equality30 for first-order coherent fields, lG(l)(xl, x ~ ) I = [G‘”(x,, X ~ ) G ‘ ’ ) ( Xx~,,) ] ~ ’ ~ ,
(9)
we obtain yet another expression for R,
R
= ( A 1 ( 2 G ( 1 ) (ttil),
+ (A2(2G(1)(t2,t z )
+ ~ [ I A I I ~ G ‘ ” ( ~~1I ) l ~ 2 1 2 G ( 1 ) (t2)]1’2 ~23 7
cos{4(ti, t 2 ) > ,
(10)
which is equivalent to Eq. (7) except for the (unimportant) suppression of 8. These results are valid for general fields (nonstationary as well as stationary) with arbitrary statistical properties (since only first-order correlation functions appear). We now direct our attention to constituent beams which are stationary. Individual first-order coherence for these fields implies monochromaticity, and the functions &*(tl) and &t2) for well-collimated, fully-polarized beams (of frequency w1 and w2, respectively) may be expressed as25 &*(t,)= [G(’)(tl, t,)]”’ exp(iw,t,)
(11)
&(t2) = [G(’)(t2,t,)]1/2 exp( - icu,t,).
(12)
and
Here again the times t l and t , are relative to the source. Using these fields, the last term in Eq. (7) may be written
2 Re{Al*&*(tl)A2&(t2)) = 2 Re{Al*A2[G(1)(tl, tl)G(’)(t2, t2)I1I2 x exp(iwltl)exp( - i u 2 t 2 ) } .
(1 3)
Inserting the product exp( - i w 2 t l )exp(iw2tl) = 1 , we obtain 2 Re(ll*b*(tl)A2&(t2)}= 2 Re{Al*A2[G(”(tl,tl)G“)(tz, t2)]1/2 x exP[i(wi - u 2 ) t i I exP[iw2(ti
- t 2 ) I ) . (14)
9.
COHERENT DETECTION IN THE INFRARED
369
For stationary constituent fields Eq. (7) thus becomes
R = lAIIZG(')(tl,t l ) + ]A2\2G(1)(tz, t2)
+ 2[G(')(t,, tl)G(')(tz, tz)]'/'
Re{Al*A2exp[i(o, - w2)tl] exp(io,T)), (15 )
where the quantity w2z = wz(tl - t z ) may be thought of as a phase difference between the beams. Since we do not have advance information about the phase of a particular beam in any experiment, however, in using the theory we should properly choose states which are averaged over phase. Although the interference term in Eq. (15) will vanish through the ensemble average in this case, the interference would be present in any individual experiment. We assume that we can select an ensemble by considering only experiments with the same phase difference. This permissible procedure is entirely analogous to that used for spatial interferen~e.'~For convenience we shall choose the phase difference w2z in such a manner as to precisely cancel the phase factors arising from A t * and ,Iz. The counting rate for a restricted ensemble such as that discussed above, and for a field possessing first-order coherence with stationary constituent beams, may therefore finally be written as R
=
IAIIZG(')(tl,t i )
+ ~A2~zG(')(tz, t2)
+ 2[1A1(2G")(tl,t1)lAz(2G(1)(t2,tz)]1'2
COS(w1 - w2)t.
(16)
The phase difference has been conveniently chosen as described above, and t , has been written as t in the interference term. We note that G(')(tl, t l ) and G(')(tz, tz)are count rates which are constant in time and do not possess any fluctuating components. In terms of the classical intensities I, and I z for the individual beams this is equivalent to R
=
I1
+ + 2(11 Iz)l/z COS(w1 - wz)t. 12
(17)
This expression differs from the usual classical result3-' in that it does not contain sum- and double-frequency components of w , and w z . This will be made more explicit later. Although the correct result may be obtained semiclassically by using the analytic the range of validity of Eq. (17) (high frequencies such that hv S kT) appears naturally in the quantum treatment. Furthermore, the quantum theory may be used to obtain an expression valid throughout the electromagnetic ~pectrum,'~ as indicated earlier. 32
L. Mandel and E. Wolf, Rev. Mod. Phys. 37,231 (1965).
370
M. C. TEICH
I t is observed from Eq. (10) that for nonstationary beams with a firstorder coherent field the interference term exists but is not sinusoidal. The result in Eq. (5) is valid even when there is not maximum fringe contrast (first-order coherence). In that case, however, the equality in Eq. (9) no longer holds, and must be replaced by the inequality3'
From this it is evident that the photomixing term will be reduced below its maximum value when there is a departure from precise first-order coherence of the total incident radiation field. Thus, optimum sinusoidal photomixing is the result of temporal and spatial first-order coherence of the total incident radiation field, and stationarity of the constituent beams.23
a. Density Operator The restriction which first-order coherence places on the density operator for the field has been discussed by Titulaer and G l a ~ b e r . ~They ' have generalized the definition of a mode to include nonmonochromatic solutions to the wave equation, and have thereby derived a density operator for the most general type of field possessing first-order coherence. This operator may be obtained by replacing the creation operator akt in the single-mode density operator by a more general creation operator h f . This latter quantity creates a photon in a particular superposition of modes which may be considered as specifying a particular type of photon wave packet. Therefore a field which has first-order coherence may be regarded as consisting of photons of only a single (in general nonmonochromatic) variety. It has also been shown that if a field possesses such a density operator, it is first-order coherent. Since any field expressible in Glauber's P-representation may be separated into a coherent and an incoherent portion, furthermore, only the coherent portion will contain photons of the variety that give rise to a heterodyne signal. The heterodyne detection process may then be considered as the annihilation of a single photon of this variety. Thus even in the presence of a single one of these photons a heterodyne signal may still be observed. As in the case of spatial i n t e r f ~ r e n c e ,therefore, ~~ D i r d c ' ~well-known ~~ comment, "Each photon interferes only with itself. Interference between two different photons never occurs," applies to the heterodyne experiment. This is not surprising, since we are considering a type of interference experiment which is a one-quantum process. For multiple photon processes, such as two33 34
R. L. Pfleegor and L. Mandel, Phys. Rev. 159, 1084 (1967); J . Opt. Snc. Am. 58, 946 (1968). P. A. M. Dirac, "Quantum Mechanics," 4th ed., Chap. I, p. 9. Oxford Univ. Press, London, 1958.
9.
COHERENT DETECTION IN THE INFRARED
371
quantum d e t e ~ t i o n ~ * , or ~ ~the - ~ Hanbury-Brown-Twiss ’~ effect, this is not necessarily true.25 b. Uncertainty Principle The uncertainty principle also shows that it is not useful to consider the photons of the constituent beams separately. In fact, in a heterodyne experiment we are unable to determine from which beam a photon is absorbed in a given time interval. Consider a description in which there are two alternate ways in which the system can evolve from its initial state to the final state : by absorption of a photon from beam 1 or by absorption of a photon from beam 2. In order to ascertain which beam gave rise to the ejection of a particular photoelectron, its energy would have to be measured to within a value A E given by AE < hlw, - w21. From the uncertainty principle
AE AT 2 h ,
(19)
the time AT required for such a measurement would be AT 2 h/AE
=
lo1-
(20)
The required measurement time is greater than the period of the beat frequency, and such a measurement would therefore wash out the time interference. Thus one cannot ascribe a detected photon to one or the other of the constituent beams. A related argument has been applied by Pfleegor and Mande133to independent beam spatial interference a t the single-photon level. c. Ciussicul Theory
In the classical theory the total electric field vector E , is given by E,
El cos(o1t)
+ E2 COS(o,f),
(21) where E l and E , are the amplitudes of the individual incident waves. Assuming that E , and E 2 have the same polarization, the count rate R, from the classical detector is proportional to the intensity of the radiation or to the square of the total electric field :
R , = E,,
=
= E l 2 cos2(w,t)
+ E , E , COS[(W,
-
+ Ez2 C O S ~ ( C J ~ ~ ) + E,E2 COS[(O, + w&].
(uZ)~]
(22)
The usual argument invoked at this point is that the detector cannot follow the instantaneous “intensity” at the sum- and double-frequency components if its resolution time is larger than the period of the radiation. Since the M. C. Teich and G. J. Wolga, Phys. Rev. 171,809 (1968). 35aM.C. Teich and P. Diament, J . Appl. Phys. 40, 625 (1969). 35bP. Diament and M. C . Teich, J . Opt. SOC. Am. 59,661 (1969). 35
372
M. C . TEICH
electron-photon correlation time36 is - 2 x 10-14sec in a metal, this providesa cutoff for the optical region. In any case, the post-detector circuitry generally has very limited frequency response, so that only averages of the first, second, and fourth terms in the above expression are observed. Thus such terms are usually ignored in the optical'-5 and in the ir~frared,~ and no contradiction with experiment is observed. However, it is clear from the quantum analysis that these rapidly varying terms never appear for the usual absorption detector when hv $- kT, and therefore would not be observed even with detectors of arbitrarily small resolving time.
2. SIGNAL-TO-NOISE RATIO A parameter which is of interest in evaluating the usefulness of a receiving technique is the signal-to-noise ratio. In this section we discuss the operation of an infrared (optical) heterodyne receiver and calculate the expected signal-to-noise ratio at the output of the detector. Considering either the quantum theory or the classical theory with the usual assumptions, the response r of the detector to the two incident waves is given by
+
r = p(&Ei2 +E2*
+ E l & cos[(wl - m2)tI) = rdc +
rlpI
(23)
where a proportionality factor fl containing the quantum efficiency is now included (previously fi was arbitrarily taken equal to 2). It is assumed that the detector has a sufficiently high frequency response to follow the signal at the difference frequency (al- 4. If we confine measurement of the signal to a band pass about the difference or heterodyne frequency (also called the intermediate frequency or IF), then it follows that r]F = PEIB2 cos[(w, - c u z ) t ] . (24)
+
However, since rdc = $(El2 EZ2),the detector response may be written in terms of its dc component :
For a very strong LO beam, which is the usual experimental condition, E 2 $- El,and it follows that rIF = 2(E1/E2)rdc Cos(wIFt). (26) The mean-square photodetector response for a sinusoidal signal is then given by ($F) = 2(Pl/P2)rk (27) 7
where P, and P2 are the radiation powers in the signal beam and LO beam, respectively. 36
P.S. Pershan and N. Bloembergen, Appl. Phys. Letters 2, 117 (1963).
9.
COHERENT DETECTION IN THE INFRARED
373
a. Photoemitter and Ideal Reverse-Biased Photodiode
If we now consider the noise response rn in the detector as arising from shot n o i ~ e , ~which ’ , ~ ~ is the case for the photoemitter and the ideal reversebiased photodiode, then the mean-square noise response is given by the well-known shot-noise formula (r”2> = 2 e r d C A .
7
(28)
“(“)
where Af is the bandwidth of the receiver. Hence the signal-to-noise ratio (S/N),,,,, may be written (S/N),,,,, = __ cr:,> = (rn2> e Af p2 However, since rdc arises from the comparatively large LO, it is related to the LO beam power P2 by the quantum efficiency q : rdc
= (qe/hv)P2.
(30)
Thus, for a sinusoidal signal, the signal-to-noise ratio become^^^,^' (S/N),,,,,
= qP,/hv Af
(photoemitter and reverse-biased photodiode). (31a)
From this relation it is seen that the value of the signal-beam radiation power necessary to achieve a (S/N),,,,, = 1 is given by
p y = hv Af/q
(photoemitter and reverse-biased photodiode). (31b)
This quantity is defined as the minimum detectable power, and is denoted by PFin.It has been assumed that experimental conditions are such that the “excess noise”39-40a above shot noise may be neglected. This is usually, but not always, true for single-mode laser sources operating well above threshold, where intensity fluctuations are quieted. If the two radiation beams impinging on the detector are not parallel to within a certain angular tolerance,16.“ and do not illuminate the same area, or the radiation is not normally incident upon the p h o t ~ d e t e c t o r , ~ ~ then (SIN) and PFinwill differ from expressions in Eqs. (31a) and (31b). The radiation beam incident on the detector must also possess first-order coherence for this result to hold.23In the experiments reported in this work the conditions required for the relations given in Eqs. (31a) and (31b) have B. M. Oliver, Proc. I.R.E. (Correspondence) 49, 1960 (1961). H. A. Haus, C. H. Townes, and B. M. Oliver, Proc. I.R.E. (Correspondence) 50, 1544 (1962). C. Freed and H. A. Haus, Phys. Rev. 141, 287 (1966). 40 J. A. Armstrong and A. W. Smith, in “Progress in Optics” (E. Wolf, ed.), p. 213. NorthHolland Pub., Amsterdam, 1967. 40sJ. J. Mezrich, Circuit Model for Amplitude Noise in Lasers. M.S. thesis, Massachusetts Institute of Technology, Cambridge, Massachussetts, January 1969 (unpublished). 4 1 V. J. Corcoran, J . Appl. Phys. 36, 1819 (1965). 4 2 A. J. Bahr, Proc. ZEEE(Correspondence) 53, 513 (1965). 37
38
’’
374
M . C. TEICH
been satisfied. For a sufficiently large LO power the theory derived in thc form given above has been experimentally verified both for the case of photoemitters5 and for back-biased photodiodes. 1 2 , * In particular, Hanlon and have recently verified Eqs. (31a) and (31b) in a bandwidth of 1 Hz using an InAs diode detector. h. Phntorondurtor and Photouoltaic Diode
For the case of a photoconductor the noise behavior differs from simple shot noise, and the results derived above arc not directly applicable. Photoconductor noise is a complicated phenomen0n,4~and depends to a great extent on the nature of the p h o t o c o n d ~ c t o r In . ~ ~the ~ limit of large LO powers, however, extrinsic Ge :Cu is expected to display simple generationrccombination (g-r) noise.45 Since the behavior for simple g-r noise is the same as that for shot noise except for a factor of t ~ o , ' -47~ it. may ~ ~ be shown that the signal-to-noise ratio for Ge:Cu has a valuc just one-half as large as that for a photoemitter or a nonleaky reverse-biased photodiode of the same quantum efficiency. The same result has also been obtained as a special case (in the absence of trapping) of a relation derived by DiDomenico and Anderson4* for CdSe. In the photovoltaic cell, on the other hand, the same processes occur as in the reversed-biased photodiode. However, instead of generating a current, a voltage results from the dipole-layer charge, since the cell is effectively open circuited. Thc detcctivity and the real noise equivalent power (RNEP) for both the reverse-biased p-n junction and the photovoltaic detector have recently been discussed by van Vliet,44 who has shown that the RNEP for the photovoltaic cell is higher than that for the reverse-biased photodiode by a factor of $. It follows that the (electronic) noise power, which is proportional to the square of the RNEP, is a factor of two greater for the photovoltaic configuration. Therefore the signal-to-noise ratio for the photovoltaic device, as for the photoconductor, is just one-half that for the photoemitter or the reverse-biased photodiode. It should be pointed out, however, that the advantage gained in signal-to-noise ratio for reverseJ. Hanlon and S.F. Jacobs, JEEE J. Quantum Electrun. 3, 242 (1967). K. M. van Vliet, A p p f . O p f .6, 1145 (1967). 44aVan Vliet44 has separated photoconductors into four classes, each of which behaves differently : intrinsic, minority trapping model, two-center model, and extrinsic. " H. Levinstein, Appl. Opt. 4, 639 ( I 965). 46 R. C. Jones, Proc. I.R.E. 47, 1841 (1959). '' A. van der Ziel, "Fluctuation Phenomena in Semi-Conductors." pp. 22. 65. Butterworths, London and Academic Press, New York, 1959. 48 M.DiDotnenico, Jr. and L. K.Anderson, Signal-to-Noise Performance of CdSe Bulk Photoconductive Detectors. Bell Telephone Lab., Murray Hill, New Jersey (unpublished memorandum). 43 44
9.
COHERENT DETECTION IN THE INFRARED
375
biased photodiode operation can only be realized for detectors having a high reverse-bias dynamic resistance, as will be seen later. The signal-to-noise ratio and minimum detectable power for the extrinsic photoconductor and for the photovoltaic junction are therefore given by (SIN),O,,,
=
vP,/2hv Af
1
(photoconductor and photovoltaic diode).
(324
PFin= ( 2 / q ) hAf. ~ (32b) These devices are a factor of two less sensitive than a photoemitter or ideal reverse-biased photojunction of the same quantum efficiency [compare Eqs.(3la)and(31b)],andafactor of2/ylesssensitivethan the perfect quantum counter. (For the photoconductor, although both the signal and the noise depend on the photoconductor gain G , the ratio may be shown to be independent of this parameter. * 3, The operation of photoconductive Ge:Cu as a heterodyne detector near the theoretical limit given by Eqs. (32a) and (32b) was demonstrated by Teich et ( ~ 1 . ~ ' Similar experiments performed on Ge:Hg by Buczek and Picusso have also been found to agree closely with the predictions of Eqs. (32a) and (32b). In later sections we discuss in detail the experimental results of heterodyne measurements on photoconductive Ge :Cu and on photovoltaic Pb, -,Sn,Se. In both of these cases the experimental agreement with the theory outlined in this section is quite good. It should be kept in mind, nonetheless, that the expressions given here have been derived explicitly for a sinusoidal heterodyne signal. Ill. Measurement of the Signal-to-Noise Ratio 3. EXPERIMENTAL ARRANGEMENT
A block diagram of the experimental arrangement used for the heterodyne measurement^',^^ in photoconductive Ge:Cu is shown in Fig. 3. The radiation from a C02-N,-He laser, with an output power of approximately 10 W at 10.6p, was incident on a modified Michelson interferometer. One mirror of the conventional interferometer was replaced by an off-center rotating aluminum wheel which had a roughened edge obtained by sandblasting. The diffusely scattered radiation from the wheel provided a Dopplershifted signal which was recombined at the beamsplitter with the unshifted 49
M. C. Teich, R. .1. Keyes, and R. H. Kingston, Appl. Phys. Letters 9, 357 ( I 966). C. J. Buczek and G. S. Picus, Appl. Phys. Letters 11, 125 (1967); G. S. Picus and C . J. Buczek, Far Infrared Laser Receiver Investigation. Hughes Res. Lab., Malibu, California, Interim Tech. Rept. No. 4, Contract AF33(615)-3487, 1967 (see also Repts. 1-3).
376
M. C . TEICH
I
I
IRIS
WIRE GRID POLA~IZER
COLD BAFFLE
ATTENUATOR
ROTATING WHEEL
BEAM
'
SPLITTER
I
,-,
/-L.O.
BEAM
Ge:Cu DETECTOR AT 4'K
2 LOAD
RESISTOR
MIRROR
FIG. 3. Experimental arrangement for heterodyne measurements with a Ge :Cudetector. The electric field vector lies perpendicular to the plane of the paper. (After Teich.')
LO radiation reflected from the mirror of the other interferometer leg. Both the mirror and the beamsplitter were cocked at a slight angle to the usual 90" and 45" (respectively) in order to prevent this reflected radiation from feeding back into the laser. Heterodyne detection measurements with scattered radiation at 0.6328 j L have been made previously by Gould et aL5' and by others.52A. E. Siegman has calculated the maximum radiation power to be returned by a random ~ c a t t e r e r . ' ~ ' ~ ~ The experimental apparatus, with the exception of the rotating wheel and the chopper, was mounted on a granite slab supported by compressed fiberglass blocks. To further reduce the effect of acoustic vibrations the 1.25-m-long Brewster window sealed laser tube was set on shock mounts and enclosed in a wooden shield paneled with acoustic tile. The laser was operated well above threshold and was very carefully tuned to operate on a single line and mode, so that no excess noise (above shot noise) was expected from the beam. This was accomplished by blocking the signal beam and then adjusting one laser mirror for a TEMoo mode and the absence of any observable beat signal. The interferometer mirror was then adjusted to give the largest signal-to-noise ratio when the signal beam was permitted to pass. Back and forth adjustments were made until a mirror position was found for which all of the above conditions were coincident. An uncoated Irtran I1 flat (of thickness 0.64 cm) served as a beamsplitter, and front surface 51
'*
G. Gould, S. F. Jacobs, J. T.LaTourette, M. Newstein, and P. Rabinowitz, Appl. Opt. 3, 648 (1964).
R. D. Kroeger, Proc. I E E E (Correspondence)53, 211 (1965); G. A. Massey, Appl. Opt. 4, 781 (1965).
53
A. E. Siegman, IEEE Trans. Antennas Propagation IS,192 (1967).
9.
I
w OSCILLOSCOPE
I
I F
C02 LASER
CHOPPER
-ni-
377
COHERENT DETECTION IN THE INFRARED
VOLTMETER
I I
ATTENUATOR
BEAM SPLITTER /
MATCHING TRANSFORMER
MIRROR&t
Pbx Sn,’-x Se DETECTOR AT 77°K
FIG. 4. Experimental arrangement for measurements with a Pb, -,Sn,Se detector. The arrangement is similar to that shown in Fig. 3, with the exception of the detector output circuitry. (After Teich.’)
mirrors were of standard aluminum-coated glass. These mirrors were highly reflective in order to prevent thermal distortion and consequent deformation of the wavefront of the reflected radiation. An Irtran I1 lens of focal length 2.54 cm was inserted in the signal beam to focus the radiation to a single point on the sandblasted rim of the rotating wheel. The purpose of the lens was twofold: It served to collect sufficient scattered radiation to permit an incoherent (nonheterodyne) measurement of the scattered signal power at the detector for calibration purposes, and it also ensured spatial coherence of the scattered radiation over the receiver aperture. This is analogous to the technique used to obtain spatially coherent thermal radiation, where the source is focused onto a pinhole aperture stop. This ensures that all points on the wavefront emanating from the pinhole arise from the same source point and are therefore correlated. The coherence properties may be deduced from the van Cittert-Zernike t h e ~ r e r n1., 5~4 Irises were used to maintain the angular alignment of the wavefronts of the two beams to within Lja, the required angular tolerance for optimum photomixing (a is the detector aperture).I6 It should be noted that this angular alignment restriction is 20 times less stringent than in the visible region of the spectrum. A Perkin-Elmer wire-grid polarizer ensured that the
’‘ M. Born and E. Wolf, “Principlesof Optics,” p. 505. Pergamon Press, Oxford, 1959.
378
M. C . TEICH
FIG. 5. Photograph of the heterodyne apparatus. (After Tcich.’)
recombined beams, which impinged normally on the photodetector, had a common linear polarization. Thc output from the detector was fed through a controlled-bandwidth, low-noise amplifier to a thermocouple-type rms voltmeter. Alternately, the signal was fed sirnultaneously to an oscilloscope and to a spectrum analyzer. The setup used for the heterodyne measurements with photovoltaic Pb, -,Sn,<Se is shown in Fig. 4. It is essentially identical to the arrangemenl for Ge :Cu, with the notable exception of the detector output circuitry. For the high-impedance photoconductor (dark resistance 600 kilohms) a 1-kilohm load resistor is used to convert the photocurrent to a voltage suitable for amplification. For the low-impedance photovoltaic device ( - 1.5 ohms), on the other hand, the voltage is both increased and transformed in impedance by thc use of a matching transformer. A photograph of the actual apparatus used in these measurements is shown in Fig. 5.
-
4. EXPERIMENTS WITH
PHOTOCONDUCTIVE
GE :C U
n. Detector Fabrication and Characteristics
The copper-doped germanium detectors used in the heterodyne experiments were made by indiffusion of Cu into high-rcsistivity n-typc gcrmanium host material for a period of 16 hr at 760°C. The samples, which were
9.
COHERENT DETECTION IN THE INFRARED
379
2 mm x 2.2 mm x 3 mm in size were then quenched in air. The resulting copper atom concentration was 6.8 x 10’5cm-3, and the compensation by the original donors was such as to produce a free-hole lifetime of about 2 x lO-’sec at 4°K. With a bias voltage of 13.5 V on the detector its (incoherent) low-power responsivity was 0.2 A/W by calibration with a blackbody source of known temperature. The detector was operated near liquid helium temperature. b . Heterodyne Operation at kHz Frequencies Figure 6(a) shows a multiple-sweep display of the heterodyne signal obtained at the detector output with a signal beam radiation power of 1 x 10- * W. The loss of definition of the waveform in the third cycle reflects the finite bandwidth of the heterodyne signal. Figure 6(b) shows a single trace of this signal for a longer time scale. The modulation bandwidth is caused by statistical fluctuations of the heterodyne signal arising from the moving diffuse surface of the wheel.
FIG.6 . (a) A multiple-sweep display of the heterodyne signal from a Ge:Cu detector. The loss of definition of the waveform in the third cycle reflects the finite bandwidth of the heterodyne signal. (b) A single-sweep of the signal shown in (a), but with a longer time scale. The modulation of the signal envelope arises from the random nature of the scattering surface. (After Teich.’)
380
M. C . TEICH
Ge:Cu DETECTOR -c0 "'-HETERODYNE FREQUENCY: 70kHz
a a do4K
W
B
- 30 mU
g ro3-
h
Y
w
z
- i o cn
0 -0 -4
0
FIG.7. The data points, obtained from a typical run, represent the observed signal-to-noise ratio of the heterodyne signal in Ge:Cu, (S/N),,,,,, for a given signal-beam radiation power (P,).The theoretical curve, given by the expression (S/N)pawer = qP$ZhvAJ is in good agreement with the data. The minimum detectable power Prin(defined as that signal beam power for which the heterodyne S/N is unity) corresponds, in a I-Hz bandwidth, to 7 x 10-20W. (After Tei~h.~)
The results of a typical experimental measurement of the heterodyne signal-to-noise ratio for the detector are shown in Fig. 7. The filled circles represent the observed signal-to-noise power ratio data points, (S/N),,,,,, as a function of the signal beam radiation power (P,or PI).Only noise arising from the presence of the single-mode, single-frequency LO beam (which was the dominant contribution to the noise) is considered. Various values of P, were obtained by inserting calibrated CaF, attenuators in the signal beam, while the unattenuated power was measured by chopping the signal beam in the absence of the LO. As indicated earlier, the presence of the lens facilitated this measurement. A plot of the theoretically expected result for a sinusoidal signal [Eq. (32a)], (S/N),ower = vPs/2hv M
9
(33)
is also shown in Fig. 7. Using an estimated quantum efficiency q = 4,it is in good agreement with the experimental data. Had noise from sources other than the LO been taken into account in computing the S I N , the
9.
COHERENT DETECTION IN THE INFRARED
381
experimental values would still be within a factor of two of the theoretical curve. Measurements were made with an LO power of 1.5 mW. With a heterodyne signal centered at about 70 kHz and an amplifier bandwidth of 270 kHz the experimentally observed minimum detectable power Prin(defined as that signal beam power for which the heterodyne SIN is unity) was 2 x 10- l4 W. In a l - H z bandwidth this corresponds to a W, which is to be compared with minimum detectable power of 7 x the expected value (2/q)hvAf
NN
7.6 x
W.
(34)
The experimental measurement is therefore within 6 dB of the theoretically perfect quantum counter, and is in substantial agreement with the expected result for the Ge:Cu detector used in the experiments. c. Noise Modulation
Because the roughness of the wheel (- 10 p) is comparable to the radiation wavelength I., the bandwidth of the noise modulation B should be given by49
B
-
vld,
(35)
where v is the velocity at which the illuminated spot traverses the surface and d is the diameter of the focused spot on the wheel (- 50 p). This follows from the fact that every d l v seconds a completely new spot on the wheel is illuminated, giving rise to scattered radiation which is uncorrelated with that of the previous time interval. The coherence time z1 is therefore
-
dlv,
(36)
since the frequency bandwidth is given by the inverse coherence time. With
v
re
(3 7)
FA/D,
(38)
=
and
d
NN
the noise-modulation bandwidth is given approximately by B
-
r8DjFA.
(39)
Here v is the tangential velocity of the wheel (157 cm/sec), d is its angular velocity ( l o x sec- I), and r its radius (5.05 cm); F represents the focal length of the lens (2.54cm), while D is the diameter of the radiation beam at the output of the laser (- 5 mm). Using these values, a calculated noise modulation bandwidth B -30
kHz
(40)
382
M . C. TElCH
I
50
I
70
I 90
f (kHz)
FIG.8. A typical power-spectral-density trace of the heterodyne signal from Ge:Cu. The trace sweep speed was 4 sec-’. The center rrequency of 70 kHz corresponds to the period of 14psec observed in Fig. 6jb). (After Teich.’)
is obtained which is comparable with the value observed on the powerspectral-density trace shown in Fig. 8. A Panoramic model SB-15a ultrasonic spectrum analyzer operated with a trace sweep speed of 254 sec- was used for the observations. A smooth, bell-shaped curve would have been obtained by integrating and then recording the power-spectral-density curve. The center frequency of 70 kHz corresponds to the period of 14 psec observed in Fig. 6(b).Both traces were obtained directly across the (1 kilohm) photoconductor load resistor. A more detailed treatment of the powerspectral-density will be given later.
d . Possible Power Dependence of Photoconductor Gain A discrepancy between the observed values of signal and noise (individually, rather than the ratio) when compared with the values calculated on the basis of the measured responsivity has not been re~olved.~’Experiments have shown, however, that the photoconductor gain depends neither on the chopping frequency of the incident radiation nor on the heterodyne frequency, a possible cause for the disagreement. Other experiments, which were performed by placing attenuators in various positions in the optical path, indicate that amplification of frequency-shifted (scattered) radiation” by the laser is not responsible for the effect. Measurements of the small-signal
’’ W. M. Doyle, W. D. Gerber. and M. B. White, I E E E J . Quantum Electran. 3,479 (1966).
9.
COHERENT DETECTION IN THE INFRARED
383
photoconductor gain as a function of the LO power were inconclusive, and it remains possible that this effect has some bearing on the problem. It appears that this discrepancy does not occur for the lead-tin selenide photodiode detectors. e. Results for Other Materials at 10.6p
The results discussed in this section are similar to those given for Ge : Cu by Teich et aE.7.49Buczek and Picusso in their experiments with Ge:Hg used two independent C 0 2 lasers oscillating at slightly different frequencies. The minimum detectable power which they obtained (referred to a 1-Hz bandwidth) was P:'"(Ge:Hg)
=
1.73 x
W,
(41)
which is in good agreement with the results obtained for Ge:Cu using a completely different experimental configuration. More recently, Mockerssa has also achieved operation near the theoretical limit in photoconductive Cd,Hg, -,Te, while Leiba55band Abrams and Glasss5chave observed the effect in pyroelectric triglycine sulphate (TGS) and in Sr -,Ba,Nb,O, (SB N), respectively. 5 . EXPERIMENTS WITH
PHOTOVOLTAIC P B 1 - ,SN,SE
a . Delector Fabricafion The Pbl -,Sn,Se diodes used as heterodyne detectors were fabricated from Bridgman-grown crystals by Melngailis and by Calawa et a1.56--58 The band gap of these diffused p-M junction devices varies with composition (x), so that the wavelength for peak responsivity may be adjusted by varying x. The devices which were used achieved their maximum responsivity (- 1 V/W, 77°K) at the C0,-laser wavelength, and had the composition Pb0.936Sn0.064Se (see Fig. 9 for a plot of the responsivity versus wavelength for a typical diode). The nature and inversion properties of the conduction and valence bands for these alloys have been discussed in detail both for the and for single-crystal thin films.s9 The inversion behavior of 5'aH. M o d *, Appl. Opt. 8, 677 (1969). 55bE. Leiba, Compt. Rend. 268B, 31 (1969). 55cR, L. Abrams and A. Glass, Appl. Phys. Lerlers 15. 251 (1969). " I. Melngailis, unpublished work (1967). " A. R. Calawa, I . Melngailis, T. C. Harman, and J. 0. Dimmock, Photovoltaic Response of Pb,-,Sn,Se Diodes, presented at the Solid State Device Res. C o d , Univ. ofcalif. at Santa Barbara, June 19-21, 1967. '* J . F. Butler, A. R. Calawa, I. Melngailis, T. C. Harman, and J. 0.Dimmock, Bull. Am. Phys. SOC.12, 384 (1967). 5 9 A. J. Strauss, Phys. Rev. 157,608 (1967).
384
M. C . TEICH
1
10.6 )r I
m w a
‘ 0.01 1
10
I I5
(v) RESPONSlVlTY OF A Pb0,9J6 Sno,0s4Se DIODE AT 77’K WAVELENGTH
FIG.9. Responsivity of a typical Pb, ,,,Sn,,,,,Se Melngaili~.’~)
diode versus wavelength at 77’K. (After
the bands in Pbl-,Sn,Se is similar to that observed for Pbl-,Sn,Te.60 The detectivity of the devices D* was
D* > 3
x lo9 cmsec-’’2 W - ’
and the carrier concentration was
- lo” ~ r n - ~ .
(42)
b. Device Characteristics
The diodes had a 1-mm diameter active area and were operated at 77°K in the photovoltaic mode. The thin n-type layer (- 10 p ) was exposed to the LO and signal beam radiation. The I-V characteristic of diode #37, both in the absence and in the presence of the LO, is shown in Fig. 10. It is seen from these curves that the zero-current impedance, as well as the reverse impedance, of the detector is x1.5sZ. This value, which is very low, is essentially independent of the presence of the LO. Using a calibrated thermopile and the I-V characteristic of Fig. 10, the quantum efficiency and responsivity for the device were directly determined to be 8.5% and 0.9 V/W, respectively. The eficiency could be further improved by depositing an 6o
J. 0.Dirnmock, I. Melngailis, and A. J. Strauss, Phys. Rev. Letters 16, 1193 (1966).
9.
COHERENT DETECTION IN THE INFRARED
385
200
100
mA
a -100
-200
-200 -100
0
100 200
mV
mA
mV
FIG.10. (a) Current-voltage (I-V) characteristic of the Pb,,,,,Sn,,,,,Se diode used in the heterodyne experiments. The upper trace is the dark characteristic, while the lower trace is the characteristic with the (18 mW) LO applied. (b) Same characteristic on expanded 1 and V scales. (After Teich.’)
antireflection coating on the diodes. The numerical values for the quantum efficiency and the responsivity are consistent with those obtained by Melngailis using a different method at much lower radiation powers. Improvements in the device characteristics subsequent to the measurements described here are mentioned in the Conclusion. c . Discussion of Experiment
The arrangement used in the heterodyne experiments (see Fig. 4) was described in detail earlier. A transformer at the output of the detector transformed its impedance to a level appropriate for matching to the lownoise amplifier. The experimental procedure was identical to that described for measurements on Ge :Cu, i.e., various values of the signal beam radiation power P, were obtained by inserting calibrated CaF, attenuators in the signal beam. The unattenuated power was determined from the known responsivity of the diode by chopping the signal beam in the absence of the LO, and then using phase-sensitive detection. In all cases the direct response
386
M . C . TEICH
of the detector was ascertained to depend linearly on the LO radiation power. In calculating the signal-to-noise ratio, only noise arising from the presence of thc LO was considered. The noise figure of the amplifier was such that with modest LO powers of 15 mW the noise associated with the LO was typically -25% of the total noise. I t appears that higher LO powers could have been used without any difficulty; however, a rearrangcmcnt of the apparatus would have been required to obtain LO powers in excess of thc value used. Experiments wcre performed in two different regions of heterodyne frequency and bandwidth : an IF of 110 kHz with a bandwidth of 65 kHz, and an IF of 2.05 MHz with a bandwidth of 10.0 MHz. They are described below.
-
d. Heterodvne Operation at kHz Frequencies A Princeton Applied Research Model AM-2 input transformer (frequcncy range 5-150 kHz, turns ratio 1 : 100) coupled thc detector output to the high-input-impedance, low-noise amplifier (PAR Model CR4-A). Measurements were madc with an LO power of 9 mW.
Pbll Snl-,Se
DETECTOR 30
50
10
-m 2
n
W
30
$ z
\
!O 10
~
,$4
,$3
16i2
10io
1c9 toa
0
i f 7
Ps ( W a t t s )
FIG. 1 1 . The solid line is the observed signal-to-noise ratio for the heterodyne signal in
Pbl_,Sn,Se as a function of the signal-beam radiation power. The heterodyne frequency is 110 kHz and the detection bandwidth is 65 kHz.The theoretical curve. (S/N),,,,,, = qP,/2Ai,A,J, lies within the limit of experimental accuracy. (After T e i ~ h . ~ )
9.
387
COHERENT DETECTION IN THE INFRARED
The results of a typical experiment are shown in Fig. 11. The solid line is the observed signal-to-noise power ratio (S/N),,,,, of the heterodyne signal as a function of the signal beam radiation power P,. With a heterodyne signal centered at 110 kHz and a transformer-amplifier bandwidth of 65 kHz the experimentally observed minimum detectable power PFin is 1.6 x 10- l4 W. The dashed line in Fig. 11 represents the theoretical result. Using the relation (S/N),,,,, = qPs/2hvAf and a quantum efficiency q = 0.085, it lies within the limits of experimental accuracy. The observed minimum detectable power corresponds, in a 1-Hz bandwidth, to 2.5 x 10- l 9 W. Since the experiments were performed using a scattering surface, however, it must be kept in mind that the observation bandwidth for the heterodyne signal must be greater than the noise modulation bandwidth (- 50 kHz for an IF of 100 kHz) for an accurate measurement of the signal-tonoise ratio. e. Heterodyne Detection at M H z Frequencies
The behavior of the Pb, -,Sn,Se heterodyne detectors at MHz frequencies was investigated by rotating the scattering wheel faster. This was accomplished by replacing the 300-rpm synchronous motor driving the scattering wheel with a 3600-rpm motor. A small matching transformer (turns ratio 1
I
Pbx S n i - x S e
DETECTOR
to” -
- 50
2 . ,a-
- 40
9
+
a w
-
k
c
THEORETICAL
9
$ to3 z
m
-30
a w
102 -
-20
-
-10
W
z
g
3 P g z
\
10’
cn
0 U
fw
loo--
-0
I
’
lO’C
! I ,0’3
I
10’2
I
II
,61’
- -10
Af = 1 0 M H z I ,OiO
I
,09
I 10-8
I
,67
I I lo-6
P, ( W a t t s ) FIG. 12. Signal-to-noise ratio as a function of signal-beam radiation power for 2.05 MHz heterodyne signal from Pbl -,Sn,Se. The agreement of theory and experiment, as in Fig. 1 1 , is good. (After Teich.’)
388
M . C. TEICH
11 :55, 30 gauge wire, on a Ferroxcube Corporation 7F160 cup core) at the output of the detector provided an impedance of approximately 50 ohms at the input of a wide-bandwidth, low-noise, integrated-circuit amplifier. The effective bandwidth of the transformer-amplifier combination was 10.0MHz. The LO power was determined from Fig. 10 (and the known responsivity of the detector) to be 18 mW. The signal-to-noise ratio for the heterodyne signal at 2.05 MHz is shown in Fig. 12. This plot is similar to that of Fig. 11, except for the IF and the bandwidth. The minimum detectable power for this experiment is 7.6 x W, which is larger than that of Fig. 11 because of the increased bandwidth. The dashed line, representing the theoretical result, predicts a value
P y x 4.8
x
w,
(43)
which is within the experimental bracket. The observed minimum detectable power, extrapolated to a 1-Hz bandwidth, is 7.6 x lO-”W, which may be compared with the expected value
(2/q)hvAf x 4.8 x 10- l 9 W.
(44)
FIG. 13. (a) A multiple-sweep display of the heterodyne signal in Pb,-,Sn,Se. The loss of definition of the waveform in the fifth cycle reflects the finite bandwidth of the signal. (b)A single sweep of the heterodyne signal shown in (a), but with a longer time scale. This figure is similar to Fig. 6 for Ge:Cu; note the very different time scales, however. (After Teich.’)
9.
COHERENT DETECTION IN THE INFRARED
389
f. Noise Modulation Figure 13(a)shows a multiple sweep display at the detector output which is similar to that shown for Ge:Cu in Fig. 6. The loss of definition of the waveform in the fifth cycle reflects the finite bandwidth of the heterodyne signal. Figure 13(b)shows a single trace of this signal for a longer time scale. Since the noise modulation bandwidth B and the heterodyne frequency are both proportional to the angular velocity of the scattering wheel 6, their ratio is independent of the IF and depends only on geometrical factors. Therefore Figs. 6 and 13 appear very much alike in spite of their very different time scales. This will be discussed quantitatively and in detail in Part IV. g. Results for Pb, -,Sn,Te
Heterodyne detection has also been observed in Pb, -,Sn,Te diodes operated in the photovoltaic m ~ d e . ~The ~ particular * ~ ~ ~alloy - ~composition ~ used had x = 0.17 (Pbo.83Sno.17Te),which has its peak response at 10.6 p when operated at 77°K. The detector output voltage was observed to be proas is portional to the square root of the signal beam power (cc &), expected for heterodyne operation. The responsivity of these preliminary diodes was too low, however, to observe the noise associated with the LO. This, of course, is necessary for optimum heterodyne detection. Recent advances in the operation of these diodes (see Chapter 4 by Melngailis and Harman) make them appear very suitable for heterodyne detection, however. IV. Detection from a Moving Diffuse Reflector Most of the measurements discussed previously have been concerned with a mean detection rate or a time-averaged value of the signal-to-noise ratio. They are therefore related specifically to the first-order coherence properties of the incident radiation. Information other than average count rates, such as the spectral distribution of the mixing signal and the probability density of its envelope, has also been obtained e~perimentally.~" Quantities such as these may be shown to depend on correlation functionsz4 of the radiation for example, have field higher than first-order, however. Freed and related the power-spectral-density of the photocurrent for a direct (nonheterodyne) detector to the second factorial moment of the photocounting distribution, and thus to a second-order correlation function of the radiation 60aM.C. Teich, unpublished. I. Melngailis and A. R. Calawa, Appl. Phys. Letters 9, 304 (1966). 6 2 I. Melngailis, A. R. Calawa, J. F. Butler, T. C. Harman, and J. 0. Dimmock, Photovoltaic Effect in Pb,Sn, -,Te Diodes, presented at the Intern. Electron Devices Meeting, Washington, D.C., October 26-28, 1966. 61
390
M. C . TEICH
I
LASER
W I R E GRID POLARIZER
OSCILLOSCOPE
t
I
MIRROR
&
Pb, Sn,-,Sa OET ECTOR AT 77'K
SPECTRUM
FIG.14. ExperimenVal arrangement for power-spectral-density and statistical measurements with a lead-tin selenide photovoltaic detector and a sandblasted aluminum scattering wheel. (Aftcr Teich.")
field. The spectral-density for the photomixing signal has been considered by Forrester6'" who obtained an expression for this quantity in terms of the spectral-densities of the light beams, for the case of Gaussian radiation. Mandel"' has considered the mixing of two independent laser modes and has arrived at an expression similar to that given by Forrester. The spectrum for the heterodyne signal is not strongly dependent on the higher-order coherence properties of the individual sources, however. In this section, the fluctuation properties of the homodyne signal arising from the scattering wheel experiments are discussed. This is generally the configuration of an infrared laser radar, as mentioned previously. In particular, we investigate the power-spectral-density of the heterodyne signal and the probability density of its envelope when the radiation oscillator is fully coherent, i.e., a single-mode stabilized laser operated well above threshold. The parameters we study provide direct information about a target, such as its velocity and its statistical nature. They are also useful in the optimum processing or transmission to a distant point of the heterodyne signal. As a simple example, the signal amplifier should be designed for minimum noise figure, and its bandwidth chosen sufficiently large to pass the heterodyne signal. Such design will, in general, depend upon both the h2aA.T. Forrester, J Opt. Sor. Am. 51, 253 (1961) h2bL Mandel, Phys. Rev. 138,8 7 5 3 (1965).
9.
COHERENT DETECTION IN THE INFRARED
391
fluctuation and spectral properties of the input signal. Information about the nature of the scattering medium may also be obtained from careful examination of the details of the homodyne signal. This is the basis of the use of the technique for heterodyne spectroscopy. For example, the homodyne return from a moving puff of steam is considerably broader in frequency than the return from a diffusely reflecting moving metallic target, as will be seen later. This results, of course, from the large velocity spread of the constituent water molecules. Further information may be obtained, in a similar way, by studying the probability density of the homodyne signal or its envelope. These quantities are much more strongly dependent on the higher-order correlation functions of the radiation field than is the photomixing spectrum. In fact, the electric field probability distribution of an unknown radiation source may be determined by the heterodyne mixing of this source with a stable oscillator, as will be shown. We first proceed to describe the details of the experimental arrangement to measure these parameters, and then present our results for the power-spectraldensity and probability distribution of the envelope of the homodyne signal.
6. EXPERIMENTAL ARRANGEMENT The experimental arrangement for these measurements is illustrated in Fig. 14. It is quite similar to the arrangement shown in Fig. 4, with the noted absence of certain components required only for measurements of the signal-to-noise ratio. All experiments described in this section were performed with the photovoltaic lead-tin selenide diode. The output of the detector was fed into a Tektronix type 585A oscilloscope for the probability density measurements, and into a Panoramic type SPA-3a spectrum analyzer for the power-spectral-density measurements. In distinction to experiments designed to measure signal-to-noise ratios, the heterodyne signal was displayed without amplification. In these experiments, the LO power was maintained at a level of approximately 18 mW, while the signal beam radiation power was sufficient (2l o p 7W) to provide a very high signal-to-noise ratio. The heterodyne signal was centered at about 2.0 MHz and had a mean voltage level of about 0.03 V. 7. POWER-SPECTRAL-DENSITY OF THE HETERODYNE SIGNAL The time trace of a typical heterodyne signal and its envelope, obtained from an oscilloscope photograph, is represented in Fig. 15. It has the appearance of a narrowband random process, i.e.,
B/v, < 1,
(45)
where B is the heterodyne signal frequency bandwidth and vD is the heterodyne or Doppler frequency (which is used interchangeably with ~ , ~ / 2 7 1The ).
392
M . C. TEICH
k 5 . 0 psec 5
FIG.15. Time trace of a typical heterodyne signal and its envelope. (After Teich.'")
quantities B and B/v, are easily calculated for 3 cases : (a) focused radiation on the rotating wheel, (b) unfocused radiation on the rotating wheel, and (c) a typical radar experiment. For a radiation spot of diameter d on the wheel, a completely new area of the wheel is illuminated every d/vl seconds, giving scattered radiation which, as before, we assume to be uncorrelated with that of the previous time interval, It should be pointed out that only the uncorrelated case is considered here, which is equivalent to taking an infinite variance for the surface roughness distribution. This model could be modified (to include a time-dependent mean and a finite variance) in order to allow for a determination of the target's mean path, or surface shape, which might be possible in some applications. Nevertheless, for the uncorrelated case, the heterodyne signal frequency bandwidth may be written as
B x: v,/d.
(46)
This is a more accurate result than that given previously in Eq. (35). The quantity ul represents the wheel velocity perpendicular to the beam axis, and is equal to v cos # where u is the tangential velocity of the wheel and 4 is the central angle shown in Fig. 14. Thus, forfocused radiation, the heterodyne signal bandwidth Bfocis given by Bfoc % (rdD/FA) cos #,
(47)
which is similar to Eq. (39) but more precise. For any reasonable value of 4,
9.
COHERENT DETECTION IN THE INFRARED
393
the contribution to the bandwidth arising from the finite spot size on the scattering wheel may be neglected in this case. The Doppler frequency vD, as is well known, is given by the relationship vD = 2~11/R= (2u/R)sin 4,
(48)
where u l l is the wheel velocity component parallel to the radiation beam axis. The ratio of bandwidth to heterodyne frequency Bfoc/vDmay then be written B,,,/vD
x (D/2F)cot 4.
(49)
This ratio depends only on geometrical factors, as has been pointed out previously. For moderate values of 4, this quantity will be less than or of the order of unity in most cases, although it may be seen that the narrowband nature of the signal will be destroyed for sufficiently small values of 4. For the case of unfocused radiation and the rotating wheel, there are two individual contributions to the finite bandwidth : the u,/d component as in the last case, and the contribution arising from the spread in Doppler frequencies over the finite spot size on the wheel. We denote this latter quantity by A v D . From Eq. (48),it is easily seen that AvD
= ( 2 A$/R) ~ cos 4
(50)
for the usual case of A 4 4 1 and thus, AVD/VD
X
Cot 4 A4.
(51)
But, since A 4 is given by the relation
Aq5 x d/(rcos (p),
(52)
where d again represents the (unfocused) spot size on the wheel, we obtain AvD/vD
x (d/r) csc 4.
(53)
The u,/d contribution is easily seen to be = (1/2d) cot 4 ,
(54)
VD
so that the total fractional frequency spread Bunfoc/vD x [(d/r)’ csc’
-
4
B u n f o c / ~ D may
+ (1/2d)’cot2
be written as
(55)
For most situations, this quantity will be smaller than unity for moderate values of 4 (e.g., for d/r 0.1, and R -4 d, Bunfoc/vD< 1 provided only 4 > 5”), so that the signal will usually possess a narrowband character in this case as well. Generally for the unfocused case, I 4 d 4 r, so that the Doppler-frequency spread will be the dominant term.
394
M . C. TEICH
We now consider the return from an infrared rudur beam tracking a moving solid target. If it is assumed that the beam sized is of the order of the target size, then the frequency broadening arising from the target’s diffuse nature will be negligible. But in analogy with the previous case treated, there will be a contribution arising from the spin or rotation of the target about an axis perpendicular to the beam direction, which gives rise to a Doppler-frequency spread. In this case, then, the center frequency of the mixing signal is given by VD =
2ull/l
(56)
= Vr
(57)
where now “11
is the radial velocity of the target as a whole. Then, an order-of-magnitude estimate of the bandwidth may be given by Bradar
-
2 ( 2 ~ r o J A )x 4r0) JJ-,
(58)
where r is the “radius” of the target, urot is its rotational velocity, and w I is the component of angular velocity perpendicular to the beam direction. Therefore, the bandwidth to Doppler frequency ratio may be written as Bradar/VD
2rco L/ur,
(59)
which indicates a narrowband signal when 2 r o , < v,. Thus, for the radar configuration discussed, the center frequency of the heterodyne signal determines the radial velocity of the target (0,) while the bandwidth of the signal may provide information about the spin or rate of rotation of the target. Coupled with the time dependence of the amplitude of the return (reflecting the infrared radar cross section), specific information may also be obtained, in principle, about the surface characteristics and shape of the target. For a beam size which is smaller than the target, on the other hand, one can scan the target to determine its velocity profile and thus its rate of rotation (e.g., the moon). The contributions would be similar to those observed for unfocused radiation falling on the scattering wheel, with the additional consideration that a center-of-mass translational radial velocity will increase the center heterodyne frequency vD. Therefore, in analogy with a microwave radar, a good deal more may be learned about a target than just the magnitude of a single one of its velocity components. The validity of Eqs. (47)and (49)above has been demonstrated experimentally with the rotating scattering wheel. For a 5.05-cm radius wheel rotating at 3600 rpm (4 = 12071sec- ’), with F = 2.54 cm, D x 5 mm, and 4 x 30”, we calculate the values Bloc = 0.3 & 0.1 MHz
(60)
9.
COHERENT DETECTION IN THE INFRARED
395
FREQUENCY ( M H z )
FIG.16. Experimentally measured power-spect ral-density of the heterodyne signal as a function of frequency. Also shown is the full-width at half-maximum (FWHM) of the curve. (After Teich l a )
and
Bft,,..\'D
=
0.17
0.05
from Eqs. (47) and (49), respectively. The experimentally measured (relative) power-spectral-density under these conditions is shown in Fig. 16. In this figure, the power-spectral-density scale is linear and the frequency resolution is approximately 0.05 MHz. The measured values of Bfoc= 0.3 MHz (FWHM) and Bfoc/vD= 0.15 are in good agreement with the predicted values above. The narrowband nature of the signal for these parameter values is most clearly displayed on a multiple-sweep display such as is shown in Fig. 13a. The loss of definition in the fifth cycle reflects the ratio Bfoc/vD. As the angle 4 is decreased (see Fig. 14), maintaining focusing of the beam on the wheel rim and the same experimental configuration, the number of cycles before loss of definition decreases, reflecting the increasing value of Bfc,c/vD(acot 4). For sufficiently small values of 6,the narrowband nature of the signal disappears, as expected, and the multiple-sweep display loses all resemblance to the kind of picture seen in Fig. 13a. On the other hand, adecrrase in the ratio B/v, has been observed by simply removing the focusing lens from the experimental arrangement leaving 4 unaltered. This operation had the effect of adding cycles to a representation such as that shown in Fig. 13a. This effect is understood on the basis of Eqs. (49) and (55), keeping in mind that for the unfocused case
dlr
+ A/2d,
(62) and that d is limited to about 2 mm by the iris aperture for these experiments. The heterodyne signal amplitude may decrease in this case, however, if the
396
M. C. TEICH
detector resolves the illuminated spot on the wheel. This has been discussed previously. Analogously, for optimum detection in a real radar experiment, the receiver aperture must be sufficiently small so as not to resolve the return signal,’ 1 * 5 2 in order to maintain spatial coherence. We have discussed the power-spectral-density of the homodyne signal in terms of the size, granularity, and configuration of the scattering target. It has not been necessary to refer specifically to the coherence properties of the scattered radiation. Such is not the case, however, if we investigate the statistical nature of the heterodyne signal or its envelope. For these parameters, it is necessary to have direct information about the statistical nature of the scattered radiation signal, or about its higher-order correlation functions. This is discussed in the next section. 8. PROBABILITY DENSITY OF
THE
SIGNAL ENVELOPE
A knowledge of the statistical behavior of the heterodyne signal is useful for the optimum processing and transmission of the signal, as well as for providing information concerning the nature of the scattering medium. Because of the narrowband nature of the homodyne signal in many cases of interest, it is useful (and practically speaking, simpler) to investigate the form of the envelope probability density function. We may then compare the theoretically expected results with those obtained from experiments with a known scatterer, and thus verify the validity of our theoretical model and method of calculation. It has been shown earlier that double- and sum-frequency heterodyne terms do not appear in the properly formulated quantum theory of infrared heterodyne detection. For radiation fields which possess a positive-definite weight function in Glauber’s P-repre~entation,~~ which is the case for all fields considered here, the heterodyne detector response may be written in terms of a semiclassical representation as cc
+ 41.
-5f”ELO COS(OJL,~)E~ COS(O~~
(63) Here, as before, rIFrepresents the photodetector response at the intermediate frequency, EL, and E , represent the magnitude of the electric field for the local oscillator (LO) and the scattered (S) beams, respectively, o the angular frequency of the particular radiation beam, and 6 is a phase angle. The operator 9 stands for the “low frequency part of.” Now, if the LO arises from a well-stabilized single-mode laser above threshold, as assumed earlier, then ELo and wLo are strictly constant. The addition of a constant phase has been omitted for simplicity. The random scattering from the rotating wheel (see Fig. 14) has the effect of converting the “coherent” incident LO radiation to narrowband Gaussian2’ radiation. This conversion of radiation statistics is similar to that obtained by inserting TIF
9.
COHERENT DETECTION IN THE INFRARED
397
a rotating ground-glass screen in the transmission path of a laser beam and is a consequence of the central-limit theorem. Such experiments have been performed by Martienssen and Spiller62cto convert deliberately a coherent laser mode to narrowband chaotic radiation in order to observe a positive Hanbury-Brown-Twiss correlation. Thus, the scattered radiation differs from the LO radiation in two respects: its frequency is altered (Doppler shifted), and its statistical properties are changed. As a consequence, the scattered beam radiation field may be represented as a narrowband Gaussian random process (centered in the infrared) and may be written in standard form62das E,(t)cos[w,t + 6(t)].From this, we rewrite rlF as
Since we obtain finally
But this expression for the homodyne signal voltage is itself, as well, in the form of a narrowband Gaussian random process. Now, however, it is centered at the Doppler frequency. Nonetheless, although both constituent beams (LO and S) are stationary, optimum sinusoidal photomixing is not obtained because the additional requirement of first-order coherence for the total incident field is satisfied only for time intervals well under a coherence time. (The detection has, nevertheless, been shown earlier to be optimum.) It is therefore seen that for an experimental arrangement such as described here, the heterodyning process effectively translates the fluctuation properties of the scattered field down to the Doppler frequency. Stated differently, the heterodyne voltage accurately reflects the scattered beam electric field distribution in a beating experiment performed with an amplitude-stabilized LO without fluctuation. Indeed, another example of this is the mixing of two strong amplitude-stabilized fields. Hinkley et ~ 1 . ~have ’ ~ mixed the radiation from a single-mode COz laser with that of a single-mode Pbl -,Sn,Te semiconductor laser operated well above threshold and obtained a sinusoidal beat signal with almost no fluctuation. The envelope of the heterodyne signal in this case has essentially a delta-function voltage probability distribution, reflecting the absence of amplitude fluctuations, and therefore, the coherent 62cW.Martienssen and E. Spiller, Am. J . Phys. 32,919 (1964). 62dW.B. Davenport, Jr. and W. L. Root, “An Introduction to the Theory of Random Signals and Noise,” p. 160. McGraw-Hill, New York, 1958. 62eE.D. Hinkley, T. C. Harman, and C. Freed, Appl. Phys. Letters 13, 49 (1968).
398
M. C. 'IEICH
nature of the signal beam. However, on reducing the diode laser power and using very careful measurement techniques,62' they have been able to measure the linewidth and Lorentzian shape of the heterodyne signal power-spectraldensity and thereby directly observe the quantum phase fluctuations in a Pb,,,sSn,,,2Te diode laser above threshold, thus verifying the form of the Schawlow-Townes formula. We note that while amplitude fluctuations (such as from the scattering wheel) will result in spectral broadening, pure phase or frequency modulation will not be observable in studies of the envelope but will, of course, be evident in the power spectrum. Thus, measurements of the signal statistics and its spectral-density provide complementary information. Hence, information about a scatterer may be obtained if the behavior of the radiation beam incident on the scatterer is known, or the fluctuations of an unknown radiation source may be studied by mixing with a stable LO. We now direct our attention to the probability density function for the homodyne signal envelope in the case of scattered radiation from the metallic wheel. As is well known, for a narrowband Gaussian random process (NBGRP),62dthis should be Rayleigh distributed. A typical trace (sample function) of the homodyne signal and its envelope has been shown in Fig. 15. The probability density of interest was experimentally obtained by sampling the envelope at 1.0psec time intervals. Some 15 oscilloscope photographs similar to the one represented in Fig. 15 were analyzed in this fashion, providing 754 data points. The envelope voltage was always taken to the nearest 0.01 V. These data are presented in the histogram of Fig. 17 where, on the relative envelope voltage scale, 1 V actually represents 0.01 V. Also plotted in the same figure is the Rayleigh density function P ( V ) = (Vb)exp(- V 2 / 2 a ) ,
(67)
which, as may be seen by inspection, fits the experimental data very well. This expected fit was confirmed by performing a chi-squared test."g A value of x 2 = 8.28 with 7 degrees of freedom was obtained, giving a probability P = 0.3 that the deviations from the Rayleigh density function would be expected to be greater than those here observed on repeating the series of measurements. This result provides strong evidence that the signal envelope may indeed be fitted by a Rayleigh distribution. The single parameter M in the distribution p ( V ) above was chosen by setting the observed average envelope voltage ( VUbJ equal to the average calculated from the Rayleigh distribution ( VRay).Performing the average,
v)
z 2
a
t>
- 0.15 v)
K
z
g 10'
W
0
m
*
0
t
LL
0 -0.10
a
w m
; a m
I
0
a
= I
n
2
5'
- 0.05
VOLTAGE (relative scale)
FIG.17. The heterodyne signal envelope probability density versus voltage. The experimental result (histogram) and the theoretical prediction (Rayleigh density function) are both shown. (After Teich.'")
and setting (Gay)
= (V b s )
>
(69)
we obtain =
(2/n)
zJb,
(2)
+ bzpc/z,.
(3)
The photoconductive gain saturates at the field which just sweeps out the minority carriers, but the gain-bandwidth product (GB = G/271zp,) continues to grow. Here ( 0 4 ) is the information bandwidth. In this extreme of carrier sweepout the photoconductor resembles a diode with ohmic contacts, which give it a small current gain equal to the ratio of the sum of the freecarrier mobilities to the pair drift m ~ b i l i t y . ~ 4. INJECTION OF MAJORITY CARRIER
Even if the minority-carrier lifetime is so short that no sweepout occurs (as in extrinsic photoconductors), the performance at high fields will be degraded by space-charge injection from the ohmic contacts.374The increase in density of majority carriers that sets in when the transit time drops to the dielectric relaxation time ,,z, will change the photoconductive lifetime in a A. Rose, RCA Rev. 12, 362 (1951). H. S. Sommers, Jr. and W. B. Teutsch, Proc. IEEE 52, 144 (1964).
438
H. S. SOWERS. JR.
way determined by the nature of the recombination process, but the gainbandwidth product is still specified. At high fields it has the limiting form
(4) where the asterisk indicates that the relaxation time is to be evaluated at the operating point.6v6aHowever, this increase of GB through the drop in the relaxation time is accompanied by a reduction of the device impedance. If the principal source of noise is the following amplifier, the usual case in broadband IR receivers, the drop in impedance at fixed current gain will reduce the SIN. G B = b/2nzzl,
111. Response of Detector -Theoretical
5. PHENOMENOLOGICAL LIMITON GAIN-BANDWIDTH PRODUCT
Before analyzing the response of the actual microwave circuit it is instructive to discuss the upper limit to the response from a phenomenological approach.' The internal gain of the photoconductor is limited to the number of reversals of the bias field in a photoconductive lifetime, since each carrier can cross the sample once per reversal,6b
G G 2fo(zpc+ 72).
(5)
The microwave bias frequency is fo. A limited additional current gain is produced by the output transformer coupling the photoconductor to the following amplifier. If Qo is the loaded Q of the circuit, the overall current gain can be G G 4fhpcQ0
(6)
and GB
2fOQoln =L f o Q o .
(7)
Comparison with Eq. (4) clarifies the advantage of microwave bias for broadband systems. In a dc circuit large gain-bandwidth requires high conductivity and low device impedance" ; with microwave bias the supply frequency sets the limit irrespective of the resistivity of the phototransducer.
' R. W. Redington, Phys. Rev. 115, 894 (1959). 6"In this chapter the trapping of majority carriers is neglected. Such trapping does not affect the low-frequency gain, but it increases the device response time and lowers GB,3.4 "At very high field, the carriers will traverse the photoconductor early in the microwave cycle, and the current will become capacitive. The detector now behaves like a photocapacitance rather than a photoresistance, but the current gain is still given by Eq. (5). The effect of the very high field is to change the phase and the harmonic content or the detector output. (See Eddolls and Wright.') "See also R. L. Williams, J . Appl. Phys. 40, 184 (1969)for compensated extrinsic case.
1 1. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR
I-#
REFLECTION CAVITY
439
CIRCULATOR
5
LIGHT INPUT (A.M.)
FIG 1 Photoconductive demodulator. Go
=
l,/ayF (After Sommers and Gatchell.’)
It is also apparent why very high bias frequency is desirable, for at fixed cavity bandwidth the limit on G B is proportional to the square of the driving frequency. Implicit in Eq. (7) is the assumption that the microwave field penetrates the photoconductor without being screened by the free carriers, which also requires high frequency, fo
’1 / 2 T d .
(8)
As a reference, the lower limit for 10-GHz bias is 20 ohm cm material. 6. ANALYSIS OF MICROWAVE EQUIVALENT CIRCUIT
The block diagram of the microwave circuit which has been most fully studied is shown in Fig. 1. The input signal F, an amplitude-modulated optical carrier, is focused on a small piece of photoconductor mounted in the gap of a reentrant cavity. The photoconductor is biased by a klystron connected to the reflection cavity through a circulator. Power reflected from the cavity passes through the circulator to a TWT and to a second detector. To operate, the coupling to the cavity is adjusted so that essentially all the bias power is absorbed in the cavity (critical coupling), only enough power being reflected to bring the second detector to the region of linear response. This requires about 1 mW of power at the second detector for a conventional video crystal diode terminated in 50 ohms. The response of the photoconductor to the light makes the impedance of the cavity follow the envelope of the optical signal, which modulates the reflection coefficient of the cavity and converts the input signal into sidebands of the microwave power returned to the TWT. These weak sidebands beat with the unmodulated microwave power, giving a homodyne action to the second detector. The video output reproduces the envelope of the optical input.
440
H. S. SOMMERS, JR.
The photoconductive gain of the circuit is defined as the gain from the optical input to the first source of circuit noise, the TWT in Fig. 1. It is the ratio of the signal current delivered to the TWT to the rate of production of photoexcited charge in the phototransducers. From first-order perturbation theory the gain can be derived as a function of frequency and circuit parameters.2-6a
where 6 is the depolarizing factor for the photoconductor in the cavity; v and t are the drift velocity and lifetime, respectively, of each photocarrier; m is the angular frequency of the signal; [E2/W11/2is a geometrical parameter, equivalent to a cavity-filling factor in paramagnetic resonance work, with E the electric field in the gap without the sample when energy W is stored in the cavity; R is the input impedance of the TWT; and Af is the bandpass of the cavity. The first bracket shows the dependence on the photoconductor. Although both carriers contribute in principle, one usually dominates. With sufficient bias field the only material parameter affecting G B is the saturated drift velocity of this carrier. The second bracket, [B2/W]'i2,is the figure of merit of the cavity used as an optical detector. It is a geometrical parameter independent of the photoconductor and the bias field. The challenge to the microwave engineer is to increase G B by increasing the cavity parameter at fixed cavity bandwidth. From its dimension, (volume)- 1/2,it is apparent that improvement comes from reducing the volume under the center post of the cavity, which must be done without increasing the capacitance of the cavity or shadowing the photoconductor. The last bracket is dictated by the application. The input impedance of the amplifier is about 50 ohms for large bandwidths, while the cavity bandpass must exceed twice the desired information bandwidth. When the microwave sidebands fall outside the bandpass of the cavity the gain plummets.
IV. Design Details 7. REENTRANT CAVITY
The cavity serves two purposes : it enhances the electric field in the region of the sample, which gives a large figure of merit, and it matches the high impedance of the sample to the low impedance of the microwave line, giving a current gain from the coupling.
11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR
441
0.
A.TRANSVERSE O P T I C A L PORT
insef f pasf
-3
6. AXIAL OPTICAL PORT
FIG.2. Two geometries for reentrant optical detector cavity. (After Sommers and Gatchell.’)
Figure 2 is a cross section of two versions of the same reentrant cavity which differ in the way that the light is admitted. In version A, the horizontal light beam enters through the sidewall of the cavity. This is a good geometry for the microwave circuit, since the current is conducted from the post through the sample to the copper cap of the cavity. It also permits a long absorption length for the photoconductor without increasing the gap height, which is an attractive feature for an extrinsic material with small optical absorption coefficient. With this geometry it is difficult to take advantage of the high absorption coefficient of intrinsic samples, which permit reduction of the sample thickness to a micron or less. Such a thin sample mounted across the gap would require a backing plate, increasing the stored energy W at fixed field. Version B, in which the light enters through a port on the axis of the cavity, permits a film of the photoconductor to be mounted flat against the end post. In principle, this should lead to very high performance, but it introduces the age-old problem of passing the light through a port which is transparent at optical frequencies and reflecting at microwave. Theoretically, the port could be closed with a wafer of a degenerate semiconductor
442
H. S. SOMMERS, JR.
with resistivity about lo-’ ohm cm, which would have a skin depth at 10GHz of 1 p and an optical absorption length much greater than this. The practical goal of mounting the film onto this semiconductor and making good contact between post and film and between semiconductor and end cap has not yet been reached. This design offers the hope of confining most of the stored energy to the phototransducer. In either cavity the resonant frequency is mainly determined by the length of the post. Reduction of the gap lowers the frequency (Fig. 3). When the gap is less than 5 0 p the effect is very large, showing that the capacitance under the post is now storing an important fraction of the electrostatic energy. Figure 3 shows various characteristics of the cavity as a function of the position of a probe 0.012cm in diameter inserted through the end cap. The curves are the resonant frequency (shown with measured points) and the derived parameters [Ez/W]’’z [Eq. (9)], and the ratio of electric field to root of exciting power. All are plotted against the magnitude of the gap between probe and post. Note that the calculated upper limit for the cavity parameter, assuming the entire capacitance to be the 0.005-cm gap under the post [see Section 22, Eq. (1211 is 6 x lo9 V/cm J”’, while the measured parameter is 1 x lo9. This indicates that the gap itself is still only a small part of the total capacitance of the cavity. 8. VARIABLE COUPLING
Two convenient types of variable coupler are a tapered waveguide beyond cutoff with a movable dielectric insert (Fig. 4), and a loop coupling in OSM coax. Either one needs a micrometer drive to give sufficient sensitivity and the mechanical stability necessary to prevent microphonics. The adjustable element must be located at the cavity to avoid storage of energy between coupler and cavity. It is difficult t o get sufficient coupling with the tapered waveguide, even when the hole through the end of the cavity is so large that the cavity almost loses reality. This coupler only works well when it couples through a hole in the end of the cavity, and then only for cavities with Qo of 200 or more. At lower Q partial success can be achieved by inserting a screw as a resonant antenna, but this is not a good solution, because of difficulties of deciphering resonances due to the cavity from those of the antenna and because of a reduction of bandwidth. The insert screw does not work with the lower cavity of Fig. 2, in which the microwave port is in the sidewall of the cavity. The loop coupling has sufficient adjustment to couple to any cavity. It also has the advantage of being an untuned element, making it easier to locate the cavity resonance. Two mechanical motions are required, one to control the depth of insertion and the other the rotation of the loop about the axis of the coax. This latter is less critical and serves as the fine control.
443
11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR m
n
0 0 *
lo?
N
(LEFT SCALE)
N
n? -
a w
I (3
z 10.;
a!
0
~
K a n
0
z W
3 W O
PARAMETERS
a
LL
0
5 I0.C
0
a
(RIGHT SCALE)
z
1-
8 W a
I
9.8
1
I
I50
100
2
GAP IN L./
FIG.3. Performance of reentrant cavity at different gap spacings.
The loop can be inserted through a hole in either the end or the sidewall of the cavity. The position of the hole is not critical, since the coupler has such a wide adjustment range, but the fit should be snug to avoid hysteresis in adjustment and microphonics. For convenience, a rotating joint is incorporated in the coaxial line.6d
T-
0.
TAPERED GUIDE 0.063
-4
2.50
1! 'i, 2.188
TEFLON INSERT FIG.4. Variable coupling in tapered +in. x 1 in. waveguide. All dimensions in inches.
hdA suitable rotating joint in OSM coax is made by Sage Laboratories, Natick, Massachusetts.
444
H. S. SOMMERS, JR.
9. SAMPLE MOUNTING
The simplest way of mounting is to cement the edge of a thin platelet of the photoconductor to a raised nub on the removable end cap and assemble the cap to the cavity with appropriate shims so that the sample touches the post. Assembly is simplified by coating the end of the post with a small ball of indium to give compliance. This geometry requires the light to enter through the side port. Although samples as small as 50 x 50 x 2 0 p can be readily mounted in this fashion, there are several drawbacks. The most serious is the difficulty of dissipating the microwave power, often milliwatts or more. The sample does have a good depolarizing factor, which may be nearly unity because the parallel component of E is continuous across a surface, but the cavity parameter is low because the sample occupies such a small part of the gap. Cavity assembly is apt to be tedious; it is much simpler if the sample is mounted on a small piston inserted through the bottom of the cavity [Fig. 2(B)]. A micrometer drive can then be used to press the piston until contact is made to the center post. Friction holds the piston in place. For smaller samples it is convenient to cement the photoconductor to a small block of insulator. Sapphire is good because of its high thermal conductivity. Metallizing the top and bottom of the sapphire helps the heat flow as well as improving the microwave circuit, since it avoids an air gap
InSb
POLE PIECE 6 A P PH IR E
InSb ON SAPPHIRE IN p WAVE C A V I T Y FIG.5. Sample mounted in gap of reentrant cavity.
1 1.
MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR
445
between pole face and dielectric. Again the depolarizing factor can be near unity, but the high dielectric constant of the sapphire increases the energy storage. Figure 5 is a photograph of a piece of InSb on sapphire assembled in a transverse cavity. The InSb has an exposed face 25 x 25 p and is 10 p thick. The cross section of sapphire is as small as could be cut with a string saw, about 53 x 5 0 p ; it extends across the pole face, which is about 200 p. 10. OPTICS The hole in a wall of the cavity (Fig. 2) permits f/4optics. The limit on the optical aperture is set by microwave leakage, a very large aperture being possible if the hole is sealed with a conducting transparent material. For the cavity with illumination through the end cap a conical light pipe would be appropriate. The photoconductor would be bonded to the small end of the pipe with a suitable transparent conducting material. Both the bonding material and the photoconductor must have higher index of refraction than the light pipe so as to avoid total internal reflection at the inner end. Approximate analysis of a conical light pipe reveals the following optical properties, but no experimental study has been reported : (1) Conical pipe : included angle of cone, 25, ; diameter of tip, d ;diameter of base, d sin B,/sin 24 ; critical angle of material of cone, 8,. (2) Optical performance : effective numerical aperture for source on cone axis, sin 8,; included angle of field for half intensity, 45,. A simple comparison can be made with the infinite conical pipe and with a perfect lens by thinking of each as a receiving antenna focusing the light onto the transducer of diameter d. For a source on the axis, the infinite cone reaches the thermodynamic limit of collection efficiency for a system with numerical aperture sin 8,. As the source moves off the axis, the gain remains constant to the field angle *5,, where the source passes outside of the cone and the gain drops discontinuously to zero. The truncated cone has only onequarter as high a forward gain, which stays constant to the same field angle k5,,but then the gain drops gradually and reaches zero at +35,; the field for half gain is +24. Finally, the perfect lens with field of view f 2 # and numerical aperture sin 8, also has forward gain one-quarter the infinite cone, but maintains constant gain to k25, where it drops abruptly to zero. Hence the truncated cone is similar to the perfect lens, the difference being that the gain of the cone drops more gradually, beginning sooner but mqintaining finite response somewhat longer. As mentioned earlier, these conclusions for the truncated light pipe are only approximate, being best for small cone angles, and the pattern complexity will increase at large cone angles.
446
H . S. SOMMERS, JR.
V. Performance Factors for Broadband Detectors 11 . FREQUENCY RESPONSE:G B
The performance of a detector at large bandwidth is indicated by the gain-bandwidth product GB. Equation (9) for the trap-free photoconductive detector with microwave bias describes a constant GB for bandwidths exceeding the roll off of Go determined by the photoconductive lifetime. In this region a tradeoff between Go and B is obtainable with a simple postdetection high-pass filter. Implicit in Eq. (9) is the assumption that B is less than the device cutoff, which is roughly half the bandpass of the microwave cavity (i.e., B < Af/2). For bandwidths less than G B the gain of the detector exceeds unity; if the pumping source does not contribute excess noise, the photoconductor should be more sensitive than a diode detector with unity gain5 Because of the high performance of microwave cavities, the cutoff frequency can be very high and the device can be useful at bandwidths well into the microwave range; with a 10-GHz pump, however, the cavity cutoff will restrict the upper limit to the low UHF. With the materials actually available for IR detectors two deviations from Eq. (9) can be expected. Some crystals, of which silicon is a good example,’ do not show a single photoconductive lifetime with a roll off of (l/w), but instead show a slow droop in gain at high frequencies. The GB product does not have a region of constant value and seems to increase slowly with bandwidth. The second departure occurs for samples that are so conductive as to screen the microwave field. The screening reduces the depolarizing factor 6 below the value determined by the dielectric constant of the lattice. This lowers GB, since it reduces G by a factor which is independent of modulation frequency. 12.
SENSITIVITY : INFORMATION
RETRIEVAL EFFICIENCY p
The sensitivity of a broadband optical receiver, which is best measured by SIN, is easily expressed in terms of the information retrieval efficiency j which is a dimensionless parameter defined in terms of the gain of the detector and noise in the receiver.2 Physically, the ratio of p of the receiver to the quantum efficiency a of the phototransducer is just the ratio of the height of a pulse due to absorption of a single photon to the rms amplitude of the zero-signal noise. The parameter p is so chosen that when the ratio @/a) exceeds unity the receiver can count single photons. This is also a sufficient condition, although not precisely necessary, that the receiver be
’ .I.R.
Haynes and .I. A. Hornbeck, “Photoconductivity Conference” (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 321. Wiley, New York, 1956.
1 1.
MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR
447
limited by noise-in-signal rather than amplifier or dark noise for all values of SIN greater than 1. Except for photomultipliers, (P/a) 4 1 because of degradation of the signal by transducer or amplifier noise. Quantitatively, the ratio of signal power to noise power for a receiver with small retrieval efficiency is SIN = (rnpF/4B)'
for
p < p,.
(10)
The critical value p, depends on the nature of the transducer, the nature and the size of the noise sources, the bandwidth, and the modulation depth of the ~ i g n a l . ~For " the photoconductor this critical value is p, A c(, the quantum efficiency ; for the junction diode or the photomultiplier it is p, G 2a. In Eq. (10) F is the average photon flux of the optical carrier, m is the modulation depth, and B is the information bandwidth. The quantity mF/4B is a reduced signal strength in photons/bit, which is a measure of signal level at any bandwidth. If the receiver has a large retrieval efficiency, SIN is linear in the signal intensity for all inputs giving greater than unity SIN, and the analogous form is SIN = m&F/4B,
for
p > /Is.
The linear dependence holds whenever SIN is limited by shot noise from the signal. The most sensitive detector will be the one with p > ps 2 1 ; such a receiver will retrieve all the information available from the incoming signal. The classic example of shot-noise-limited performance is the photomultiplier, which follows Eq. (11) provided that the modulation frequency of the signal is appropriate for the tube. Except for this, the shot-noise limit is not reached at low signal level, and Eq. (10) describes the performance of all other detectors (i.e., photoconductors, optical diodes, bolometers, etc.). The parameter p has a characteristic variation with information bandwidth which can be readily predicted from the definition. At narrow band'"The value /3 = /{ 1). At very low levels the photomultiplier will have the better S I N , but here reception is so noisy that the improved performance is of little practical importance.
: 0.1 implies an excess noise of around 20 dB at lo4 Hz. It has an approximately l/ospectrum. This excess noise is associated with the klystron, but not in a fundamental way. It seems to be due to failure to hold the klystron frequency close enough to the resonant frequency of the cavity, which gives a conversion of FM noise of the klystron to AM noise by the discriminator action of the cavity. Only when this source of noise is removed will the performance be limited
464
H. S. SOMMERS, JR
by the more fundamental sources of noise : amplifier noise, generationrecombination noise, and, ultimately, noise-in-signal.
22.
INCREASE IN
GAIN-BANDWIDTH
The two available parameters determining the gain-bandwidth product [Eq. (9)] are the maximum drift velocity of the carriers and the cavity performance parameter. With the exception of InSb, carrier drift velocities saturate at about lo7 cm/sec, and so it is doubtful if any new material will give much improvement. Material work will reduce the free-carrier concentration toward the limit assumed in the analysis, but the screening by free carriers is harder to avoid as the development extends farther into the IR. There is much improvement possible in the cavity parameter before fundamental limits are reached. The ideal cavity would concentrate all the electric field in the photoconductor, which would then resemble a planeparallel capacitor filled with dielectric and having no fringing field. Now the sample should be treated as integral with the cavity, and the cavity parameter would be (Ez/W)"2= [E2/$CV2]'/2= (87t x 1012/EAd)1/2,
(12)
where E is the relative dielectric constant of the photoconductor, A and d are its area across the post and its thickness, respectively, and I/ is the voltage drop across the gap for the internal field E. With diffraction-limited optics and an intrinsic photoconductor with high optical absorption coefficient the transducer size might be reduced to a cube of 5 p on edge, which would give a cavity parameter of 10" V/cm J'l2. Since this is two orders of magnitude higher than the measured parameter of the empty cavity, there is still much leeway for imaginative engineering.
23.
INCREASE IN OPTICAL
FIELD OF VIEW
So far the emphasis has been on improved sensitivity. An important practical consideration is the field of view of the detector; the larger the field, the easier the detector is to use. For a simple lens the included angle of view is the ratio of detector width to focal length. A large detector area is required to give a large field of view with a large-diameter lens. From experience with other detectors fl (which is proportional to the reciprocal of the noise-equivalent-power) should vary as the reciprocal of the detector width. l4 Achieving this is another problem in cavity design, requiring scaling the post dimensions and gap to encompass a larger-area photoconductor. The cavity parameter will also drop, hopefully by no l4
R. Clark Jones, Proc. Z.R.E. 47, 1495 (1959).
11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETEClVR
465
more than the reciprocal width of the photoconductor. Lower microwave frequency and a larger cavity may be preferred. This change would be consonant, since the larger device will have a reduced GB and so a smaller bandwidth.
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CHAPTER 12
Imaging and Display Robert Sehr Rainer Zuleeg
I . INTRODUCTION . . . . . . . . . . . . . . I . General . . . . . . . . . . . . . . . 2 . History . . . . . . . . . . . . . . . I1 . BEAM-SCANNED I MAGI NG DEVICES . . . . . . . . . 3 . The Vidicon. . . . . . . . . . . . . . 4 . The Plumbicon . . . . . . . . . . . . . 5. The Sicon . . . . . . . . . . . . . . 6 . Infrared Sensitive Vidicon . . . . . . . . . . 7 . Laser Scanned M O S Device . . . . . . . . . 111. ELECTRONICALLY SCANNED PHOTODETECTOR ARRAYS. . . 8 . Photosensitive Structures and Their Applicability to Imaging 9 . Monolithic Structures . . . . . . . . . . . 10. Thin-Film Polycrystalline Imaging Arrays . . . . . 1v. IMAGE READOUT METHODS FOR PHOTODETECTOR ARRAYS. . 1 1 . Photocurrent Mode . . . . . . . . . . . I2 . Photon Fiux Integrution Mode . . . . . . . . 13. Excitation Storage Mode . . . . . . . . . . 14. Random Access . . . . . . . . . . . . . V . IMAGING CHARACTERISTICS OF PHOTODETECTOR ARRAYS . . VI . ARRAY AND SCANNING CIRCUIT INTEGRATION . . . . . VII . DISPLAY DEVICES. . . . . . . . . . . . . 13. Ferroelectric-Controlled Electroluminescent Display . . 16. Scanned Electroluminescent Diode Array . . . . . VIII . PARALLEL READOUT IMAGECONVERTERS . . . . . . . 17 . Nonregenerative Image Converters . . . . . . 18. Pseudoregenerative Image Converter . . . . . .
. . . . . . . . . . . . . .
.
.
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467 467 468 470 470 474 474 477 480 483 483 487 493 497 497 499 504 504 505 508 508 509 514 520 521 524
I . Introduction 1 . GENERAL Electrooptical imaging and the instantaneous transmission of images from inaccessible or distant places emerged as a technological challenge from the discovery of the photoelectric effect of selenium. Today. almost 100 years later. a complete “first generation” solution to this problem has been provided in the form of television.
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ROBERT SEHR AND RAINER ZULEEG
Providing increased accessibility and range for visual perception is only a part of the overall goal of broadening human sensory perception. Imaging as an intelligence gathering process is not confined to the visible portion of the spectrum. It is of interest from the ultraviolet (UV) to the microwave part of the electromagnetic spectrum. The principal factors determining the spectral region of interest for imaging are : (1) the spectral emission, reflection, and absorption characteristics of the target scene, and (2) the wavelength of the scene illuminating source (sun, incandescent light, laser, etc), and the spectral absorption characteristics of the transmission medium. It is within this frame of reference that terrestrial temperatures between 250 and 2500°K and the wavelength of high energy density lasers combine with the transmission characteristics of the earth’s atmosphere to render the spectral region between 0.5 and 30 p a region of high information content for passive and active’ imaging under various terrestrial conditions. Consequently, the extension of optical imaging beyond the visible into selected bands of the infrared spectrum between 1 and 40p is a major objective of modern solid-state device technology. This chapter deals with the principles of solid-state imaging techniques and discusses practical devices and their characteristics. Emphasis is placed on electronically scanned planar devices fabricated from monocrystalline materials. Parts 111-VI cover this subject in detail. Beam scanned devices in which photoconductivity is the image converting mechanism are briefly treated in Part 11. Image conversion and visible display techniques by scanned electroluminescent panels are treated in Parts VII and VJII. 2. HISTORY With the discovery of the photoconductive property of selenium in I873 by Willoughby Smith’ a basis was given for the rather old and fascinating idea of “instantaneous transport of optical images.” Only two years later R. Carey proposed the first image sensor in the form of a mosaic consisting of a large number of minute selenium cells, thus imitating the human eye. However, the first actual device was built thirty years later by Rignoux and Fournier2a in 1906. They constructed a photodetector array consisting of 64 individual selenium cells, each connected by two wires to a corresponding shutter. A simple image such as a numeral projected on the
’ In active imaging the scene i s illuminated by a light source from the imaging position, and the image is formed with the reflected radiation. No special light source is used in passive imaging W. Smith, Nature (February, 1873). ”P. Rignoux and G. Fournier, Reu. Gen. Elec. 1,23 (1906).
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469
matrixzb was converted by the elements into electrical currents which operated the shutters. Illuminated from behind, the array of shutters reproduced the pattern. The idea of dissecting the picture into small elements, converting the illumination of each element into electric current, and transmitting each through a separate wire (channel) simultaneously, leads to an impractically complicated transmission system for high element density arrays. Therefore parallel (or simultaneous) readout of the image was soon replaced by serial (or sequential) readout. Already in 1884 Nipkow3 .proposed to sample (scan) the image, point after point, in a time-sequential manner by means of a rotating disk with holes precisely located on a one-turn spiral. However, this scheme has the disadvantage of severely reducing the illumination level of the image. To reproduce time-varying images sharply for the human eye, all image elements have to be sampled in less than 1/20 sec, a time interval within which the eye cannot distinguish optical changes. Thus for a 300-line frame, i.e., a 90,000-element image, the rotating Nipkow disk exposes each picture element only 1/1,800,000 sec. This difficulty was overcome with the invention of the iconoscope by Zworykin4 around 1930. The image sensing target of this device is exposed to the picture all the time, and the photoelectric image conversion mechanism is continuously active rather than only during readout time. In other words, the photon flux, constituting the incident image, is integrated during the exposure time just as in the human eye. In the iconoscope the image is converted into a stored charge pattern by means of a photoemissive instead of a photoconductive layer. The stored charge pattern is sampled and erased by an electron beam. Several other image tubes utilizing photoemissive targets, such as the image orthicon and image dissector tube, have improved on the characteristics of the original icono~cope,~ especially with respect to sensitivity, by orders of magnitude. Photoconductivity as the principally utilized effect for imaging returned with the introduction of the vidicon6 in 1950. Its major advantage was greater simplicity, ruggedness, and longer life. However, it had severe shortcomings with respect to sensitivity and speed of response. These were eliminated in later versions introduced under the names of Plumbicon and Sicon (see Part 11). ZbTheterms array and matrix will be used interchangeably throughout this chapter. P. Nipkow, German Patent No. 30105, January, 1884. V. K. Zworykin, Proc. I.R.E. 22, 16(1934). Consult D. G. Fink, “Television Engineering.” McGraw-Hill, New York, 1960, for a description of various television cameras and their operating principles. P. K. Weimer, S. V. Fourge, and R. R. Goodrich, Electronics 23, 70 (1950).
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ROBERT SEHR A N D RAINER ZULEEG
Parallel to the development of improved image tubes in the 1960's allsolid-state imaging devices began to emerge from the laboratories as a direct result of advances in silicon technology. Sophisticated microelectronic processing techniques allowed not only the fabrication of planar detector arrays of relatively high density, but also of large scale integrated switching arrays required for scanning. As with most other solid-state devices, their advantages in relation to tube devices are smaller volume, weight, and power consumption, and greater reliability under certain extreme operating conditions such as high acceleration rates. But beyond being merely a replacement for tube devices, solid-state imaging arrays are gaining importance for their two major features : ( 1 ) devices are planar, and therefore highly flexible in system applications; and (2) the spectral response can be extended to the intermediate infrared spectrum, where critical imaging requirements have so far gone unsatisfied.
11. Beam-Scanned Imaging Devices
3. THEVIDICON Beam-scanned imaging devices of the vidicon type are historically and logically the forerunners of the planar, all-solid-state, electronically scanned devices which will be treated in detail in Parts 111-VII. The scanning electron beam can be considered as a multipath switch, connecting and disconnecting serially the image elements of the target film so that the image information can be transmitted sequentially through the transmission channel. The vidicon may be divided into three sections, as shown in Fig. 1 : the electron gun section, the scanning section, and the target section. The electron gun produces, by means of a thermionic cathode and associated electrodes, a focused beam of electrons which strikes the photoconductive layer of the target. The scanning action of the beam is achieved by periodic deflections, either magnetically or electrostatically. The target consists of a high resistivity photoconductor layer applied over a transparent electrode onto the flat glass faceplate. The high resistivity photoconductor layer and the transparent electrode (signal plate) form a capacitor which is connected to the target voltage, + V,, viu the load resistor R,. The photoconductive target layer is a continuous semiconductor film which is not divided into separate image elements, as is the case with the photocathode in the iconoscope. Nevertheless, because of its high lateral resistance, the film behaves as if it consists of separate image points of the size of the electron beam cross section.
471
12. IMAGING AND DISPLAY Target section,
gun section-
Scanning section ,Glass
face plate
Photoconductive layer
Electron beam
Video signal, v, out
FIG. 1. Schematic drawing of a vidicon imaging tube, showing the major elements of the device
The equivalent circuit of an image element of the target plate is a capacitor Ci in parallel with a photocurrent generator Gi, as shown in Fig. 2. In operation the capacitors Ci are periodically connected to the target voltage V, by the electron beam, and a charge Qi = V,Ci is thus stored. Signal electrode
/
/
Image element
I
I_
-I
0 VS
FIG.2. Equivalent circuit for the vidicon.
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ROBERT SEHR AND RAINER ZULEEG
During the frame time T,-the time elapsing before the beam returns to the same picture element-C, partially discharges, owing to the photocurrent IK(Li)which has been generated by the illumination Li. When the electron beam returns to the same element it must replenish an amount of charge AQi = AVCi, which depends on the illumination level Li. A charging current i s , proportional to AV, flows each time the beam completes the circuit containing an element. This current causes a corresponding voltage difference across the load resistor R,, and consequently the signal voltage V, is a sequential, electrical replica of the various illumination levels of the optical image. The vidicon operates in the charge storage mode. That is to say, the optical image is converted into a stored charge pattern which is periodically scanned and erased by the electron beam. Erasing the charge pattern creates the video signal. Because the photoelectrical conversion mechanism is operative all the time, i.e., during scan time to as well as sample (or discharge) time t , (Fig. 3), this mode of operation is sometimes also referred to as photon flux integration mode. Charge storage mode operation in a vidicon places a basic requirement on the semiconductor film-namely, that the relaxation time of the photoelectrons be much greater-than the frame period tF, which is usually greater than 1/25 sec. If this condition were not fulfilled, the image points would diffuse laterally, and contrast would be “washed out.” As a consequence of this requirement, a simple criterion for a photoconductor applicable to vidicon targets may be given. It states that the dark resistivity should be higher than 10l2ohm cm. Resistivities of this magnitude and slow chargecarrier relaxation are usually found in semiconductors with deep lying trapping states, which cause the dark conductivity to be small through charge compensation and reduction of mobility. Electron beam
EB
1
o n t
3
I
I to------I
I ’
TF
ic= Sample time
1
= ;t
Scan time
rF=Frame period
Time, T
T;=
Somple frequency
FIG.3. Definition of time intervals in the scan cycle.
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The semiconductor compound first used in vidicon targets was antimony trisulfide7 Sb,S3, which kept its unique position for more than ten years. It is applied in polycrystalline form by evaporation onto the target plate. Depending on evaporating conditions, its dark resistivity ranges from 10' to l O I 3 ohm cm, and the onset of nonlinear, space charge limited dark current (I,, K V 2 )lies between 5 and 15 V. The space charge current limits the target voltage and thus the sensitivity of the device. However, the most undesirable feature of Sb,S3 is its slow photoresponse at low illumination levels, which limits its use for video pickup. Much work has been directed toward finding more sensitive, fast response materials or configurations for vidicon targets. These are discussed in the following subsections. Vidicon with CdSe Target
Although vacuum deposited CdSe films had been considered quite early for vidicon application, their high dark conductivity prevented actual use. Shimizu and Kiuchi* found that selenium vacancies in the film were a major cause for the space charge limited dark current. By treating the film in selenium vapor they obtained acceptable dark resistivity at the usual target field strength of about lo5 V/cm. With a CdSe target thus prepared they measured a sensitivity of more than ten times that of a Sb2S3target In contrast to Sb2S3, which is a p-type photoconductor, CdSe is n-type. It is therefore necessary to explain the detection process differently for the two materials8 When the p-type Sb2S3 is illuminated electron-hole pairs are created. The holes, as majority carriers, travel under the influence of the electrostatic field, E = Q/Cd (d is the thickness of the film), to the back side of the film and render the surface potential more positive. This potential increment is neutralized by the scanning electron beam so that the potential decreases to its initial value. In the CdSe film under illumination photoexited holes are captured by existing recombination centers, thereby neutralizing a corresponding amount of space charge of trapped electrons. This is accompanied by the rise of the surface potential at the surface exposed to the electron beam, which allows more electrons to flow into the layer during the sample time. The electron flow through the layer during the sample time (see Fig. 3) will cease when the free electrons and the trapped holes combine. The associated current gain is given by
G
=
Z,/T,,
(1)
where z, is the lifetime of the electrons in the semiconductor and T, the transit time through the film.
' S. V. Fourge, R. R. Goodrich, and A. D. Cope, R C A Rev. 12, 335 (1951). K. Shimizu and Y. Kiuchi, Japan J . Appl. Phys. 6, 1089 (1967).
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ROBERT SEHR AND RAINER ZULEEG
4. THEPLUMBICON A new type of vidicon having high sensitivity, speed, and resolution was introduced under the name Plumbicon' in 1964. The higher performance of this device is due to the p-i-n layer structure of the target film. The high, built-in electric field exerted across the intrinsic layer by the p and n contacts assures that almost all charge carriers generated in the i layer contribute to the photocurrent across the junction within their lifetime. According to Eq. (l), this results in a high current gain and consequently high photoelectric sensitivity. Photoresponse, being proportional to the carrier transit time, also improves, since the latter increases with the field strength, which is high across the intrinsic i layer. The Plumbicon target consists of a PbO layer on a SnOz layer, which form a unit consisting of three sublayers, each of different conduction type. The inner sublayer is almost pure PbO, which is an intrinsic semiconductor, while the surface layer exposed to the scanning electron beam is doped p-type. The intimate contact with the SnO, on the other side gives rise to a thin n-type layer in the PbO. The p and n layers are kept very thin, so that the intrinsic layer takes up most of the overall thickness of the PbO layer and most of the absorbed photons are stopped there. In other words, in operation, when the electron beam scans the p-type surface the photoconducting layer of the Plumbicon target constitutes a reverse-biased p i - n diode. The dark current is the low reverse current through this diode. The high sensitivity is a consequence of high photon absorption in the intrinsic layer and high carrier collecting efficiency through the built-in field. One particularly desirable feature of an imaging device is image fidelity, i.e., the proportionality of the output signal, here photocurrent I,, with luminous flux L. In general, an equation of the form
I , = CLY (2) holds true, where C is a constant and 0 < y d 1. Figure 4 shows the measured relationship between I,, and L for a Plumbicon. The top line refers to unfiltered illumination ( W ) ,while the lower three curves are obtained with red (R),green (G), and blue ( B ) filters. Plotted in log-log presentation this relationship appears as a straight line. This means y has a single value, close to unity, for the Plumbicon over its entire dynamic range. In contrast, the value of y is a function of L for the conventional vidicon. 5 . THESICON
In the original vidicon the photosensitive target is a semi-insulating photoconductor with relatively low sensitivity and slow response. In the Plumbicon
' E. F. DeHaan, A. Van Der Drift, and P. M. Schampers, Philips Tech. Reo. 25, 133 (1964).
12.
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IMAGING AND DISPLAY
10
5
t 5 2 0 01
2
5
+L
10-3
2
5
10-2
2
lirn)
FIG.4. The measured variation of photocurrent in a Plumbicon as a function of luminous flux L. Here W , R, G, and B refer to unfiltered illumination and illumination through red, green, and blue filters, respectively.
the performance characteristics are upgraded through the use of a large area, graded p i - n junction, but high resistivity is still associated with each layer. Carrying the idea of a junction structure as the photosensitive target a step further, a new device with superior performance was demonstrated in the form of the Sicon." Here the target consists of an array of electrically isolated, reverse-biased diodes each representing one image element. This device has several important features. 1. The dark current and the photocurrent can be made independent of the target (reverse-bias) voltage to result in a response characteristic with y = 1. 2. The time constant associated with the charge storage in an array of reverse-biased diodes can be made very much larger than the relaxation time of the photocarriers in the bulk, provided the material lends itself to p - n junction fabrication. 3. Electron beam bombardment and intense light spots do not affect target performance. 4. Higher speed and sensitivity of response can be achieved.
The long charge storage time constant that can be obtained with isolated diode arrays is particularly important, since it implies that such a device can be made with a long wave photoresponse without cooling the target below 300°K. Whereas in a bulk photoconductor vidicon target the charge lo
M. H. Crowell, T. M. Buck, E. F. Labuda, J. V. Dalton, and E. J. Walsh, Bell System Tech. J . 46,491 (1967); Proc. Intern. Solid Stare Circuits Conj 1967, p. 128 (1967).
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ROBERT SEHR AND RAINER ZULEEG
decay time T,, is given by6 Tb
= EEop
(3)
7
and for the open-circuited diode it is given by" where IR is the reverse leakage current, E and e0 are the dielectric constant and the permittivity of free space, respectively, p,, is the electron mobility, p is the resistivity, and I/ is the applied voltage. It is immediately apparent that high resistivity is required for vidicon operation with bulk photoconductors, while the isolated junction vidicon target calls for low resistivity. Since it is almost always possible to obtain low resistivity from intrinsic (high resistivity) material by doping, a large number of semiconductors may be adaptable for junction structures in vidicon targets. Furthermore, intrinsic semiconductors with band gaps less than 1.5eV, whose resistivities are less than 10"ohmcm at room temperature due to thermal activation, may qualify, and thus provide vidicon targets with infrared response. It must, however, be borne in mind that the resistivity p in Eq. (4)cannot be reduced indiscriminately. The breakdown efectric field strength F , sets a lower limit to p and thereby an upper limit to t d .With the lower limit for td fixed by the charge storage time, Asec, required for a frame period, Wendland" has given a criterion for the resistivity of a material to be applicable to diode array vidicon targets :
Any semiconductor in which a junction can be formed and which satisfies the inequality of Eq. (5) can be used for a charge storage vidicon target. For germanium the criterion of Eq. (5) is not quite met, but for silicon it is. The actual target structure used by Crowell et d . ' O is shown in Fig. 5. The target consists of a 540 x 540 diode array with center-to-center spacing of 20 p which is about half the diameter of the electron beam. The p-type islands are formed by boron diffusion through 8 p holes in the S i 0 2 film. Ohmic contact to the array is obtained by a gold ring evaporated onto the N region at the perimeter of the wafer. In order to make the target self-supporting and at the same time provide the optimum thickness for sensitivity, which is governed by the carrier collection efficiency, the completely processed diode array is etched on the illuminated side to thickness of less than 1.5 mil in the center area, leaving a rim about 4 mil thick for structural support. An antireflection coating on the etched surface reduces light losses. +
"
P.H. Wendland, IEEE Trans. Electron Dev. 14, 285 (1967).
12. IMAGING AND DISPLAY
477
"-region
-
substrate
1
I
I
mage
FIG.5. Schematic view of Sicon target. (After Crowell et al.")
In operation the scanning electron beam periodically charges the p-type islands down to cathode potential, while the potential of the n-type wafer is held to a constant voltage between 5 and 10 V. The SiO, film, also charged to cathode potential by the beam, remains there and isolates the substrate wafer from the beam. The incident light associated with the image is absorbed in the silicon, creating electron-hole pairs. The minority carriers (holes) then diffuse to the depletion region of the diodes, discharge the diodes by an amount proportional to the light intensity. The recharging of the diodes by the scanning beam creates the video signal. Based on a simplified model in which the p regions of the array are replaced by one large area p-layer with no lateral conductivity, the collection efficiency q, i.e., the ratio of collected holes to photon-generated holes, was calculated." Assuming a minority-carrier lifetime of approximately 10 psec, a surface recombination velocity of about lo4 cm/sec, and a wafer thickness of around 10-3cm, gives 4 x SO% for uniform illumination with visible light. 6. INFRARED SENSITIVE VIDICON
Image readout from a vidicon requires that the stored charge pattern decay with time constant T larger than the frame period zF (see Fig. 3), which is usually taken as b s e c . From Eq. (3) it is easily verified that bulk photoconductive targets require a resistivity of 10" ohm cm or more to meet this condition. Since resistivities of this magnitude are not obtainable from semiconductors with band gaps of less than 1.5 eV at room temperature,
478
ROBERT SEHR AND RAINER ZULEEG
it follows that wavelength response beyond A (p) = 1.24/Eg(eV) x 0.8 ,u is not possible without cooling the photoconductive target. It should be noted that this statement applies also to materials which contain impurity levels separated by 1.5eV or less from the band edge, since at 300°K a large enough fraction of these levels will be thermally ionized to produce sufficient free carriers to diffuse the stored image. Another effect of thermally freed charge carriers on a semiconductor imaging target must be considered too-namely, their limitation on the dynamic range of the device. Consider the case where the stored charge pattern is due to ionization of donor levels in the energy gap. If because of the target temperature a large fraction of these levels has been emptied, a photon flux corresponding to a low light level will produce a saturated response, and higher light levels cannot be sensed. To avoid saturation, the following relation must be satisfied" :
n,
+
< Nd,
(6)
where n, is the number of electrons per cubic centimeter in the conduction band due to target temperature, n, is the number of electrons per cubic centimeter excited by the radiation to be detected, and Nd the number of donors per cubic centimeter. It can easily be shown from semiconductor statistics (see, e.g., Blakemore' 3, that this relation leads to the condition Nd
> N c exp[(Ed - EF)/kT1.
(7)
Since N, , the degeneracy concentration of the conduction band, will always be larger than the donor concentration N , , condition (7) states that for a target temperature T the Fermi level E , must lie appreciably below the donor level Ed. If-as in most semiconductors-the electron mass is larger than the hole mass, the Fermi level moves upward with temperature, and will thereby reduce the dynamic range of the device. For intrinsic semiconductors as targets Gebel" gives a minimum gap energy of 0.05 eV for 300°K operation ; however, this certainly cannot be obtained in practice, because it represents the limit toward degeneracy. In the use of bulk photoconductivity for charge-storage vidicon operation condition (6) is automatically taken care of, but it may become a limiting condition for isolated junction array targets. A vidicon with spectral response between 1.0 and 2.5 p has been developed by Redington and Van Heerden14 using a gold-doped silicon target cooled close to liquid nitrogen temperature. Other silicon dopants, such as Ga, R. K. H. Gebel, Adoan. Electron. Electron Phys. 16,461 (1962).
'' J. S. Blakemore, "Semiconductor Statistics," p. 122 ff. Pergamon Press, Oxford, 1962.
l4
R. W. Redington and P. J. van Heerden, J . Opt. Soc. Am. 49,997 (1959).
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Bi, and In, were also investigated, with little success. Unsatisfactory results were also obtained with Cu-, Au-, Ag-, and Te-doped germanium. The authors point out that at liquid nitrogen the response should extend to 5 p. For 20°K they predict a response t o about 35 p. Because of the limited doping concentration allowed by condition (6), semiconductors have a necessarily low absorption coefficient in the extrinsic regime. Increasing the absorption by using very thick targets provides no remedy, since both resolution and target capacitance are inversely related to thickness. Resolution suffers because of the sideways diffusion of carriers (image washout), while target capacitance limits the voltage excursions of the video signal. An infrared vidicon requires cooling not only of the target and its surrounding structure, but the target must also be shielded from the infrared radiation emanating from the thermionic cathode which emits the scanning electron beam. The apparatus of Redington and van Heerden is shown in Fig. 6. The electron beam is deflected by two sets of hemispherical deflection electrodes and follows a circular or elliptical path through them. The arrangement and shape of these electrodes permit the electron beam to strike the target perpendicularly. Photocurrent resulting from radiation
Electron gun 1 FIG.6. Demountable infrared vidicon tube. (After Redington and van Heerden. 14)
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ROBERT SEHR A N D RAINER ZULEEG
8
1.6
12
2.0
2.4
Wovelength ( p )
FIG.7. Ahsolute sensitivity, in electrons per photon, of a gold-doped silicon target versus wavelength. The rise of the curve toward shorter wavelength is due to increased light absorption, while the subsequent drop at longer wavelength i s due to decreased collection efficiency of photoelectrons. (After Redington and van Heerden.I4)
from the cathode could not be detected with a copper-doped germanium detector in place of the target. The target was a 1.5-cm-diam, 1.0-mm-thick Si :Au wafer clamped in position with indium pads for good thermal and mechanical contact. The absolute spectral response of a Si:Au target is shown in Fig. 7. The peak at the short wavelength end demonstrates the effect of volume excitation, while the decrease of response toward the long wavelength end shows that carriers generated near the surface are not contributing to photoconductivity during their lifetime.
7. LASER-SCANNED MOS DEVICE An interesting and novel approach to infrared imaging has been reported by Phelan and D i r n m 0 ~ k . In I ~ their experiment an InSb structure consisting of a semitransparent metal film-oxide layer-n-type InSb sandwich cooled to 77°K uses a scanning laser beam instead of an electron beam for readout. The infrared image focused onto the wafer was confined to radiation between 4 and 5 p and had an incident power density of 100 pW/cm2. The other side of the wafer, with the transparent metal film surface, was continuously scanned in two directions with a 0.63-11 helium-neon laser. With a vertical scan frequency of 1 kHz and a 10 kHz frequency in the horizontal direction, a continuous oscilloscope display was obtained. The 1-mW laser Is
R. J. Phelan and J. 0. Dimmock, A p p l . Phys. Letters 11, 359 (1967)
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/-
He-Ne Laser
481
SphericalJ focusing mirror
_f
Laser scanned imaging system
FIG.8. Experimental setup for infrared imaging by means of a laser-scanned metal-oxidesemiconductor device. (After Phelan and Dimmock.L5)
beam was focused to a spot about 0.3 mm in diameter. The experimental arrangement is shown in Fig. 8. The deflection of the laser beam was accomplished by two rotating mirrors which were synchronized with the sweep frequencies of the oscilloscope. The detection of an infrared image in the vicinity of 5 p relies on the nonlinear photovoltaic response of the depletion region in the InSb near the oxide interface. For an ideal diode the open-circuit photovoltage is proportional to the logarithm of photocurrent. The incident laser beam saturates a spot on the detector which is electrically isolated from neighboring areas by the high resistivity of the depletion region. With no image on the detector each spot yields the same signal to the external load because the spot voltage is driven to depletion region saturation. Since each spot represents a capacitor coupled to the semitransparent metal electrode, just as in the vidicon, there will be no output signal as the laser passes from one spot to the next, and one spot signal decreases as the next increases. If an
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ROBERT SEHR AND RAINER ZULEEG
FIG.9. An oscilloscope image obtained with the experimental imaging arrangement of Fig. 8. (After Phelan and D i m m o ~ k . ' ~ )
image element of the detector, defined by the laser spot size, has an infrared signal incident on it, this element will contribute less response voltage as the laser scans across it because there is less voltage change from driving the element to saturation. It is this voltage imbalanze which drives a current through the external load and thus provides the video signal. It is interesting t o note that while the vidicon target is operated as a photocurrent generator with high internal resistance (Section g), the laser-scanned MOS target operates essentially in the (almost) open-circuit photovoltaic mode. A photograph of an oscilloscope display is shown in Fig. 9. The height of the letters of the image was 3 m m on the detector, whose active area measured 2 cm in diameter. The device was not externally biased, but rather relied on the field effect bias originating from the trapped charges in the oxide and at the oxidesemiconductor interface. Actually, the scanning laser beam enhances the amount of trapped charge and fixes it at a steady-state value. The MOS detector described above can also be used for infrared image storage by operating it under different conditions. Image storage for over 1 hr has been observed. The interested reader will find further details on this operating mode in the original paper.I5
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111. Electronically Scanned Photodetector Arrays
8. PHOTOSENSITIVE STRUCTURES AND THEIR APPLICABILITY TO IMAGING In electronically scanned imaging devices an array of switches replaces the sequentially sampling beam of beam scanned devices. By proper sequencing of the switching array any element of the detector matrix can be connected to a readout line in any desired sequence. Of course, for arbitrary, or truly random access, of any detector element or subarray, important for certain applications, not only the sequencing of the switching array, but the latter itself becomes rather complex (see Section 14). Another difference with respect to the vidicon is the geometrical definition of the image element in the imaging target. While in beam scanned devices the image is defined by the sampling-beam diameter, in electronically sampled detector matrices the image element is defined by individual and separate photodetector elements. These elements may be photoconductors, photodiodes, or transistors. However, the application of a particular detector element to imaging depends on its operating characteristics and the methods used to fabricate it. The latter may impose restrictions on the array fabrication, the former on the scanning circuitry. The simplest configuration of a photoconductor element is a bar cut out of single-crystal material, or a thin film of vapor deposited material on a suitable substrate, which in either case is provided with two ohmic contacts. Figures 10a and lob, respectively, give the basic geometries. The bar-type structure has been extensively used for extrinsic infrared detectors of Ge doped with Hg, Cu, Cd, and some
OHMIC metal contact
I
Substrate
\
(b)
FIG.10. Structures of semiconductor photoconductors. (a) Bar-type photoconductor element (Ge or Si): (b) thin-film photoconductor element (PbSe or CdSe): and (c) planar (diffused) photoconductor element.
484
ROBERT SEHR AND RAINER ZULEEG
other impurities. The thin-film type is primarily useful with vapor deposited photoconductors such as CdS, CdSe, and/or deposited PbSe using a wet process. A planar version of a photoconductor element is shown in cross section in Fig. 10. It consists of a vapor diffused n-type layer with defined geometry and doping level. The element is isolated from the substrate by the formed p n junction. Ohmic contacts are provided on the top surface by an N + diffusion, which is then contacted by evaporated aluminum. Thermally grown SiOz serves as a diffusion mask and as passivation. The structures of Figs. 10a and 1Oc have been employed by SorefI6 to evaluate the extrinsic photoconductivity properties of silicon. His experimental results on extrinsic photoconductors of Si :B, Si :Al, Si :Ga, Si :P, Si :As, and Si :S.b indicate that these materials are equivalent to the doped germanium photoconductors, such as Ge :Cu and Ge :Hg. Spectral response to near- and intermediate infrared (0.6-30 p ) radiation is obtainable, and a theoretical spectral response of background-limited doped silicon photoconductors is presented in Fig. 11. It is expected that the doped silicon photoconductors will yield the same infrared sensitivity, speed of response, and maximum operating temperature for peak sensitivity as doped germanium photoconductors now in use. Practical advantages over doped germanium photoconductors are cost, reproducibility, and ease of fabrication of complex arrays. These advantages are a result of the highly advanced fabrication technology of silicon planar devices as applied to device integration for microcircuits. Photoconductor elements lend themselves especially well to the fabrication of imaging matrices with spectral response in the visible and infrared part of the spectrum, i.e., for imaging in spectral bands where semiconductors have to be used which do not permit p-n-junction formation. They are best applied in polycrystalline form and exhibit peak detection capability at the temperatures below 100°K which are required for infrared imaging. Photodiodes and transistors are impaired at these low temperatures in their functioning as detectors, since they rely on fully ionized impurities and sufficient lifetime of minority carriers for proper operation. Photodiodes and transistors for imaging matrices are fabricated by planar technology. The cross section of these devices is shown in Fig. 12. The diode can either be used as a photocurrent electric cell, or a photovoltaic cell. The photocurrent cell is essentially a reverse-biased junction, and the induced photocurrent I , , is additive to the reverse or “dark” leakage current l o . In this configuration the photodiode is a current generator with high internal resistance. When the diode is operated in the photovoltaic mode it is essentially open-circuited, and the incident light develops a photovoltage ‘I’
R. A. Soref, J . Appl. Phys. 38, 5201 (1967).
12.
485
IMAGING AND DISPLAY
1 300°K background
',
/
/
-si
/
P
B
----I
--
SI Sb
I
I
I
I
I
4
6
10
20
40
Wavelength
(pi)
FIG. 11. Theoretical spectral response for six species of background-limited doped-silicon photoconductors. (After Soref.16)
across the terminals. The equivalent circuit is then a voltage generator with an emf in series with a comparatively low resistance. The open-circuit voltage V,, varies linearly with light intensity at low light levels, but vaiies logarithmically at high light levels. The logarithmic response at high light intensities is a characteristic which is utilized in lightmeters. Since the Emitter
(0)
Collector
(b)
FIG.12. Planar silicon structures. (a) Photodiode: and (b) n-p-n phototransistor.
406
ROBERT SEHR AND RAINER ZULEEG
photovoltaic effect results in moderately small signal voltages, the photocurrent mode is preferred in most electronic applications, where the photocurrent is measured across a reasonably large load resistance. This circuit arrangement produces a voltage output in ranges which are practical for electronic applications with large signal-to-noise ratios. An important parameter of a photodiode or detector is its quantum efficiency q. If the photon flux rate in photons/sec/cm’ at a wavelength /z is incident on a device, then the quantum efficiency is defined by
where I , is the diode photocurrent, A the diode area, and y the electron charge. Quantum efficiencies in silicon diodes range in the visible spectrum typically from 50 to 90%. A phototransistor in the n-p-n configuration is shown in Fig. 12b, where the actual photodiode is the collector-base junction. In the phototransistor the collector junction current I , is equivalent to the photocurrent of a single photodiode, but is amplified by the common emitter short-circuit current gain p of the bipolar transistor. Thus the collector current I , can be represented by I , = (1
+ fi)lD.
(9)
The phototransistor operates normally in a grounded emitter configuration with a floating base. Base current is introduced by the photocurrent emanating from the collector diode. Defining the quantum efficiency of a phototransistor by uT = I , / ~ ( D A , where , A , is the collector area, it follows from Eqs. (8) and (9) that VT
=
(1 + f i ) q D ?
(10)
which is the efficiency of the normal photodiode multiplied by the (1 + fi) factor. The sensitivity of the phototransistor is therefore considerably enhanced over that of the photodiode. The foregoing comparison shows that the phototransistor provides the highest sensitivity for imaging matrices, but requires more elaborate fabrication techniques. As a result, uniformity of response is expected to be not as good as in imaging matrices of photoconductors or diodes. There are two different approaches to the fabrication of imaging matrices : The monolithic array of phototransistors, diodes, or conductors, which is confined to monocrystalline material, and the thin-film array, for which a large number of semiconductor materials qualify.
487
12. IMAGING AND DISPLAY 9. MONOLITHIC STRUCTURES a . Undoped Silicon Arrays
The rapid advancement of silicon planar technology in recent years has made it possible to fabricate large numbers of active devices on one wafer (large-scale integration-LSI). A major reason for bringing this development about is the fact that silicon most easily grows an oxide film on its surface under controlled conditions, which provides a natural passivation barrier, or, in conjunction with the photolithographic process, a diffusion mask for the repeated diffusion processes necessary in device array fabrication. A perspective cross section through a phototransistor array, indicating the basic design as well as the necessary processing steps in the fabrication of the device, is shown in Fig. 13a. The equivalent electrical circuit is given in Fig. 13b. A photodiode array would look similar except for one missing n diffusion, namely, that for the n-type emitters. Starting material for the array is a p-type silicon substrate of about 0.5 ohm cm resistivity onto which an n layer 1&15 p thick and a resistivity of 0.54.7 ohm cm is grown epita~ially.'~ A diffusion of p-type walls all Collector columns _3
Emitter rows
SIOZ insulation not shown (0)
I
l
l
I
Y"
(b)
FIG. 13. Phototransistor matrix. (a) Perspective view of design : and (b) equivalent-circuit representation.
'' M. A. Schuster and W. F. List, Trans. Met. SOC.A I M E 236,375 (1966).
488
ROBERT SEHR AND RAINER ZULEEG
FIG.14. A 64 x 64 phototransistor matrix with p -njunction isolation of collector columns. ( a ) Matrix mounted and bonded to circuit board. 64 x 64 elements contained within f x f i n . squared; and (b) enlarged portion of matrix. Devices spaced on 5-mil centers (McDonnell Douglas Corporation).
the way through to the substrate follows t o separate the n layer into strips. Then the individual transistor bases are formed by p-diffusion. The final diffusion step is n-type to produce the transistor emitters within the area of the bases. Evaporated aluminum strips connect all emitters in a row, while all collectors in a column are internally connected by the epitaxiallygrown n strips. Contact to these is made a t the column end through diffused n+ bonding pads. At the crossover points of the A1 strips with the p-type isolation walls a SiOz film serves as isolation between the two. A photograph of an actual 64 x 64 element array, mounted on a circuit board, is shown in Fig. 14. Center-to-center spacing of the individual elements is 5 mil. Contacts to the odd and even rows and columns of this experimental device are made by thermocompression bonding of 1-mil-diam gold wires. It is quite obvious that the step and repeat operations, which are initiated by high precision photomasking, require accuracies of less than 0.1 mil
12.
IMAGING AND DISPLAY
489
FIG15. Imaging system performance. Photographs from monitors of 100 x 128 (upper) and 200 x 256 (lower) element matrices (courtesy of Westinghouse Electric Corporation). (After Anders et al.")
la
R. A. Anders, D. E. Callahan, W. F. List, D. H. McCann, and M. E. Wing, Western Electronic Show and Convention, 1967, Paper 13/1.
490
ROBERT SEHR AND RAINER ZULEEG
otherwise, geometrical definition of the image element suffers, as consequently, does uniformity of response. Another possible source of nonuniform response from the various elements of the array is material or diffusion inhomogeneity. Therefore epitaxial growth and diffusion must be carried out under well-controlled conditions. Phototransistor matrices from 10 x 10 to 200 x 256 elements have been from various laboratories. The imaging quality of these devices is illustrated in Figs. 15 and 16, which are photographs of television displays with video input from the detector arrays. The upper and lower “portraits” in Fig. 15 were taken with 100 x 128 and 200 x 256 element arrays, respectively. The light lines are due to an emitter short” in the corresponding rows. Figure 16 shows images of letters and symbols imaged by a 10 x 10matrix from a positive or negative black and white transparency. A gray scale pattern made from a neutral density filter with areas of 100, 80,64, and 51% transmittance is also shown to demonstrate gray level discrimination. Besides the array of isolated phototransistors shown in Fig. 13, other device configurations have been used. In particular, Dyck and Weckler” describe various monolithic designs combining p n diodes with MOS transistors and n-p-n phototransistors with MOS transistors. The latter combination has the advantage of not requiring isolation between the devices, thereby eliminating crossover interconnections and crosstalk arising from it. This will be discussed more fully in Section 12. b. Doped Silicon Arrays for Intermediate IR Imaging
It was pointed out in Section 6 that thermally generated charge carriers will limit the photoresponse and dynamic range of an imaging device [see Eq. (7)]. If the free-electron concentration n,, e.g., places the Fermi level at the temperature T within 2kT of the conduction band edge, degeneracy sets in, and a light signal incident on the device certainly will not be detected. To reduce the free-carrier concentration and thus permit photogeneration of carriers, the temperature must be lowered. By doing this, however, the minority-carrier lifetime decreases rapidly, thus prohibiting the use of junction photodetectors based upon bipolar current flow at temperatures below 100°K for most semiconductors and in particular for silicon devices. On the other hand, to obtain photoresponse over a reasonable dynamic range for radiation with wavelength longer than 5 p, temperatures below l9
’’
P. J. W. Nobel, IEEE Trans. Electron Deu. 15,202 (1968). R. H. Dyck and G. P. Weckler, l E E E Truns. Electron Deu. 15, 196 (1968). A. F. Behle, P. Y. Chao, H. Speer, and S. H. Watanabe, Proc. Microelectron. Symp. 1968, p. C2, St. Louis, Missouri (1968).
12. IMAGING AND DISPLAY
Gray scale
491
on lOxl0
loo% 6 4%
8 0O/O
5 1 o/o Transmittance
Symbol "PLUS"
on
FIG.16. Image display of 10 x 10 phototransistor matrix (McDonnell Douglas Corporation).
about 100°K are imperative. This limits semiconductor-imaging devices applicable for the near and intermediate wavelength IR spectrum to the photoconductor element only. SorefZ2has described such an array sensitive between 2 and 30 p fabricated from boron-doped silicon. Other semiconductors such as Ge :Au, Ge :Cu, Hg,Cd, -,Te, Pb,Sn, -,Te, and Pb,Sn, -,Se also show photoresponse in this spectral region, but either do not match the ease of processing which silicon does (as already mentioned at the beginning of Section 9a) or are not yet well enough known with respect to their chemical and metallurgical properties. A perspective view of part of the array is shown in Fig. 17. The design of this array elegantly solves the ever-present problem of crosstalk between
** R. A. Soref, I E E E Trans. Electron Dew 15,209 (1968).
492
ROBERT SEHR AND RAINER ZULEEG
FIG.17. Monolithic photoconductor imaging array: (a) Perspective view of part of the array: [b) equivalent circuit for array; (c) cross section through an element: and (d) equivalent circuit for individual element. (After Soref.”)
individual array elements by placing a p n junction in series with each photoconductor element. The asymmetrical current-voltage characteristic of the diode substantially reduces the current in the nonaddressed elements. The addressed element has such a polarity during readout as to forward-bias the series diode, giving optimum detector output. With a quantum efficiency of 7% at 10.6 p and a response time of about 0.2 psec the detectivity per element was calculated to be D* = 1 x lo8 cm Hz”’W-’. The measurements were made at a temperature of 25°K. These experimental results are very encouraging and indicate the possibility of obtaining high-resolution imaging matrices for the infrared region. A direct readout of the individual picture element is possible by electronically scanning the X-Y matrix. Application of the charge storage mode (see Section 13) can be utilized to improve the sensitivity. The MOST switching element combined with the photoconductor may offer new integration aspects, since it is capable of operating at cryogenic temp e r a t u r e ~ .To ~ avoid interconnect problems among the matrix, the scanning circuitry, and the amplifier circuits, it will be advantageous to integrate the whole system and operate it in the cold environment. 23
R. A. Soref, Intern. Electron Dev. Conf., Paper 5.7. Washington, D.C., October 1967.
12. IMAGING
AND DISPLAY
493
c . Imaging Arrays with Narrow-Gap Semiconductors
With the rapid advancement of semiconductor technology narrow-gap compound semiconductors of the III-V, II-VI, and IV-VI families are obtained in more exacting stoichiometry and are processed with better controlled techniques. The formation of p-n junctions by diffusion or by vapor and liquid phase epitaxy may result in the fabrication of diode arrays.z3a Indium antimonide, with an energy gap of 0.18 eV and a photoresponse threshold of 6.8 p is a promising material. Ten-element linear modules have been fabricatedz4 which can be mounted on alumina substrates to form arrays of 100 elements or more. This technique of fabricating an array has limitations of about 100 ,u per element with a separation gap of 25 p. The detectivity of such an InSb detector element was measured as a function of wavelength at 77°K with 27t sr of 300°K background. A typical peak detectivity of 4.5 x 10" cm Hzl/' W-' at 5 p was obtained,24 which is very close to the theoretical background-limited detectivity of about 6.5 x 10" cm HZ"' W - ' for this element. Presently under investigation and development are ternary compounds of lead-tin-telluride, lead-tin-selenide, and mercury-cadmium-telluride detectors. Further development of these materials is required in the photomechanical work process to facilitate photodetector array fabrication for immediate infrared imaging. The relevant research necessary to produce such a solid-state intermediate infrared imaging system will probably be oriented toward achieving the overall materials-to-scanning context and will be aimed at the optimum use of the existing photolithographic and photomechanical integration capabilities. 10. THIN-FILM POLYCRYSTALLINE IMAGING ARRAYS
The monolithic imaging array fabrication described so far is a byproduct of large scale integration techniques developed especially for silicon. As such, it is at the present to a large degree restricted to this material, or at least to a semiconductor whose chemistry and metallurgy is well understood. With other materials solid-state imaging devices can be fabricated by evaporation of polycrystalline films. The major advantage offered by this approach is the high element density and large area coverage that can be obtained with high uniformity. Its principal drawback lies in the nature of the polycrystalline material itself, in that it does not yield basic parameters such as mobility, lifetime, etc., as good as in monocrystalline material, and Z3"Ionimplantation appears less suitable for planar junction formation in infrared detectors, because resulting surface damage increases the surface recombination rate of photongenerated charge carriers. 24 F. D. Morten and R. E. J. King, lnfrared Phys. 8, 9 (1968).
494
ROBERT SEHR AND RAINER ZULEEG
Element being
scanned
Column of
tronsistors
FIG. 18. Equivalent circuit for the completely integrated 180 x 180 element array, showing method for attaching scan generators and coupling out the video signal. Storage of excited carriers in the photoconductor provides light integration. (After Weimer P I d.”)
thereby yields devices of lower u priori performance. Another problem is time stability of the device characteristics, but this can be overcome through proper passivation methods. Weimer2’ has pioneered the thin-film transistor (TFT), and was also first in fabricating a TFT integrated circuit26 containing lo5 elements. In combining thin-film photoconductors as shown in Fig. 10b with TFT’s he has subsequently devised a self-scanned imaging matrix having 32,400 imaging elements2’ Integrated with the matrix on the same glass substrate are two 180-stage shift-register scan generators and associated video coupling transistors. Figure 18 gives the equivalent circuit for the completely integrated 180 x 180 element array and indicates the method of connecting scan generators and video output. The imaging array can be operated in the charge storage mode as well as in a mode particular to this device, termed “excitation storage mode,” which will be discussed in Section 13. The diode switches, necessary for 25
26
P. K. Weimer, Proc. 1.R.E. 50, 1462 (1962). P. K . Weimer, Proc. I E E E 52, 1479 (1964). P. K.Weimer, G. Sadasiv, J. E. Meyer, Jr., L. Meray-Horvath, and W. S. Pike, Pmc. IEEE
*’
55, 1591 (1967).
12.
IMAGING AND DISPLAY
495
FIG. 19. Photograph of a completely integrated image sensor comprising the photosensitive array, the horizontal and vertical scan generator, and the video coupling circuit (courtesy of RCA). (After Weimer et a!.")
excitation storage, are incorporated into the matrix by a proper sequence of the deposited layers. The photoconductive elements consist of CdS or CdS-CdSe mixture to which an ohmic contact is formed by overlying indium or aluminum on one end and a rectifying contact on the other end by a tellurium layer. For readout the tellurium contact is biased positively, and thus presents a low resistance path for the excitation stored signal from the phot oconductor. Figure 19 shows the actual and completely integrated imaging sensor. The center-to-center spacing between elements in the array is 2 mils. The picture quality produced by this imaging sensor can be assessed from Fig. 20, which is a photograph of a television monitor with video input from a 125 x 140 element thin-film array. The advantages of large, thin-film, integrated scanning circuits combined with the image-sensing matrix on a common substrate are obvious when cost and complexity of the imaging system are considered and compared with monolithic silicon integrated circuits. Laboratory thin-film integrated circuit techniques have mastered the complexity required for combining the scanning circuit and the image sensor on one common substrate, which
496
ROBERT SEHR AND RAINER ZULEEG
FIG.20. Picture transmitted by scanning 125 x 140 elements on an image sensor. The vertical scan is at standard tv rates, and the display is on a tv monitor (courtesy of RCA). (After Weimer e f 0 1 . ~ ' )
cannot be equaled with large scale integration of bipolar transistors. Silicon MOST integrated circuits will probably rival the thin-film approach eventually, and it is conceivable that technology improvements will yield monolithic-silicon photosensor arrays which are complemented by scanning circuitry and video processing circuits on the same substrate. So far the thin-film technique has not advanced beyond the laboratory stage, and the devices and circuits are plagued by drift and deterioration of electrical characteristics with time. Continued research and development may eventually overcome the device stability problems, and thin-film passive and active elements may then become practical for complex integrated circuits for all solid-state vidicons of photosensitive element density between lo5 and lo6. An alternative to the all thin-film approach of image sensor arrays combined with the associated circuitry is conceivable which avoids the instability problems of the TFT's and takes advantage of the polycrystalline thin-film photosensor array, This design employs a silicon single crystal substrate which contains the peripheral MOST scanning circuitry and video coupling circuitry flanking the four sides of a deposited polycrystalline photosensor mosaic. The designer would have the freedom of selecting the deposited photosensitive material for a specific imaging response in a desired spectral region.
12.
IMAGING AND DISPLAY
497
IV. Image Readout Methods for Photodetector Arrays There are two principally different methods for transforming the twodimensional set of photoelectric information bits into a time sequential set of signal bits for one-channel transmission t o the display device or some other electronic data processor. These are: (1) the photocurrent mode, and (2) the charge storage mode (or photon flux integration). However, depending on the particulars of the imaging array, such as the characteristics of the individual array element (sensitivity, internal impedance, etc.) and the manner of their integration (isolated in one direction or none), there are variations of (1) and (2). Thus a recently developed technique in connection with the thin-film array27 may be added: (3) the excitation storage mode. Corresponding to these readout modes there are variations of the switching circuits which accomplish these functions. 1 I . PHOTOCURRENT MODE
In this conceptually simplest mode an element of the array is connected with one terminal to a battery and the other to ground via a switch and a limiting resistor. Image readout is achieved by sequentially switching each element from ground to the input terminal of a high-gain current amplifier. The photocurrent from each element, flowing only during the sample time, provides the video signal. The simplest mechanization of this scheme is shown for a linear array in Fig. 21. All floating-base phototransistors are tied to ground through a 3-V collector supply. The single-pole, double-throw switches keep all elements grounded through a 300-ohm resistor, except the one element whose current is read out through the amplifier. The amplifier yields an output voltage V,,, proportional to R I , , where I, = (1 + @Zp, which is proportional to the light intensity according to Eq. (9). The switching function has been implemented by MOS as well as bipolar transistors. Photocurrent readout has also been applied to planar using p n junction isolation techniques such as shown in Fig. 13. Here all collectors of the n-p-n phototransistors are common to a column, which are the X outputs, and all emitters are common to a row, the Y outputs. Thus the crossed common collector columns and emitter rows provide access to any individual element. with respect to response Matrices of various geometries were inve~tjgated'~ characteristics and speed of the photocurrent mode. The result shows that this readout mode can be very ambiguous when the phototransistors are integrated into high element density matrices. Nevertheless they yield a true photocurrent readout when all the elements are grounded except the one being sampled. In this case crosstalk is minimized. However, switching
498
ROBERT SEHR AND RAINER ZULEEG I
I I
I
I
I
I I
I
I I
I
+' -It+-
_3"+
Collector supply
I I I I
i I
Linear array of N-P-N pholo tronsistors
I I
Current amplifier
Swiiches (commutator)
FIG.21. Current-mode readout of linear
p
pi
phototramistor array.
from one column to the next introduces large transient responses which limit the scan rate. At moderate light intensities this transient requires up to 5 psec before it subsides to the steady-state photocurrent. Figure 22 shows a sample response of one element taken on a 64 x 64 matrix. The initial voltage spike is due to the load condition of the measuring circuit, and simply consists of an RC time constant when the device is in the "dark." This time limitation on the load, with R , = 10 kilohms and V, = + 3 V, is presented in the decaying dashed curve. During illumination with 50 ft-cd, the device response rises as shown by the dashed curve, leveling off at the steady-state value. Since sampling can only be done after the decay time, where static and dynamic response have a one-to-one correspondence, the current mode readout has a basic speed limitation. Consequently, at a fixed frame rate the total number of elements which can be sampled in one complete frame is limited.
Fici. 22. Sampling response of phototransistor in a matrix. Horizontal: 5 pecldiv: vertical: 2.5 jiA/div: illumination: SO ft-cd.
12.
499
IMAGING AND DISPLAY
12. PHOTON FLUX INTEGRATION MODE
The readout mode corresponding t o the charge storage mode in the vidicon is termed photon flux integration. It was first described by Weckler” and offers the advantages of increased photosensitivity and scanning speed. In this mode of operation the sensitivity of the solid-state transistor array is superior to the vidicon. As in the vidicon charge storage mode, so in the photon flux integration mode, each element is active throughout the frame time. The p-n junction diode storage mode operation is described by aid of Fig. 23. When the diode is charged to Yothrough a perfect switch the voltage decay V ( t ) under open-circuit conditions is related only to material and junction properties and is independent of junction area. For V (t )k 0 it can be shown2’ that
The variable second term on the right-hand side of Eq. (11) is related to the generation-recombinat ion current by Igpr = (Aqni/2T,)W,
(12)
and the capacitance C of the assumed linear graded junction by
c=A(~uE~E,~/~~)~/~T/-~’~,
(13)
and the depletion layer or space-charge width
(0)
t, =Sampling time To = Scan time t o = Reciprocal of sample frequency
(b)
FIG.23. Storage-mode operation of a p-n junction. (a) Ideal circuit: and (b) sampling and storage sequence. (After Weckler.”) 28
G . P. Weckler, I E E E J . Solid-State Circuits 2, 65 (1967).
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ROBERT SEHR AND RAINER ZULEEG
In the above equations W is equal to the space-charge width, A is the junction area, q is the electron charge, n, is the intrinsic carrier concentration, u is the linear doping gradient, and zo is the effective lifetime in the space-charge region. Planar silicon technology yields pn junctions which hold the charging voltage with less than 10% loss for several seconds in the dark. With reasonable values of zo from 5 to 10psec usually less than 1% decay of voltage is encountered for millisecond lengths of time. If the diode is illuminated, the photocurrent I , = 1,AH (15) (with I , the photosensitivity of the diode, A the photosensitive area, and
N the illumination level) adds to the diode dark current Ig+. As a consequence of the increased current, a more rapid discharge of the junction capacitance occurs. For sufficiently short integration times or high illumination levels the generation-recombination “dark” leakage current I,, may be neglected, and the voltage as a function of time and illumination level isz8 V ( t )= [v
y - 310H(12/yuEZE02)1’3t]3/2
.
(16)
Theoretical relations like Eq. (16)and correlation with experimental measurements are presented in Fig. 24 for V, = IOV, u = 3 x loz9m-4, and I, = 0.048 A/m2/ft-cd.
H in ft-cd L
I
I
3
FIG.24. Measured and calculated voltage decay characteristic or an open-circuited, reversebiased p - n junction for several values of incident illumination. (After Weckler.28)
12.
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IMAGING AND DISPLAY
Compared to the photocurrent mode, where each array element is exposed (and thus active) to the light only during the sample time t,, the photon flux integration mode provides an effective gain Geff given by2* Geff =
1 + (hk)?
(17)
where to is the scan time. Since t,/t, is a large number, this gain can be very high. At the same time, variations of the scan time by electronic adjustments in the scan circuit allow one to vary the sensitivity. The limit in sensitivity and gain is imposed by the finite charge time necessary for charging the pn junction capacity of a diode. Sampling times of 0.1-0.2 p e c per element are practical for photodiode or phototransistor arrays operated in the photon flux integration mode. Minimum and maximum illumination levels have been reported for representative devicesz8: Hmin z 0.02 ft-cd, and H,,, x 6.6 x lo5 ft-cd. This may be compared with Hminx 0.1 ft-cd for the current mode set by the dark current, and H,,, x lo3 ft-cd set by the saturation level of the photocurrent. Thus the dynamic range of the photon flux integration mode is about three orders of magnitude larger. Several practical storage mode structures have been developed28 and described. The combination of the p-n junction photodiode and the switch can be realized in an integrated structure with a p-channel MOST (metaloxide-semiconductor-transistor). Since the photodiode and the source diode are in parallel, it is possible to combine both diodes without affecting the operation of the structure. This is shown pictorially in Fig. 25. The combined structure then allows integration to closely spaced arrays of photodetectors. A linear array of photodiodes and MOST switches and its layout is shown in Fig. 26. Recharge readout
Sampling voltage
I
+
N
I
I
T iRL I
o
i
Charging1 voltaae
1
(a)
(b)
FIG. 25. Practical circuit for storage mode operation of a p-n junction photodetector. (a) separated photodiode and MOST switch: and (b) combined photodiode and MOST switch. (After Weckler.28)
502
ROBERT SEHR AND RAINER ZULEEC
Common ground
Common drain
Photc diode
Control gates
1
z
(a)
(b)
FIG 26. Linear integrated photodetector array for photon flux integration mode operation. (a) Integration topology of linear photodetector array: and (b) circuit representation of linear integrated circuit. (After Weckler.28)
Elements of an imaging matrix operating in the PFI mode must possess the three functional elements of: (1) a charge storage element, (2) a current generator and output proportional to the incident illumination level, and (3) a nearly ideal switch. It is therefore possible to use a p-n junction as the switching element. A normal phototransistor can be utilized and operated in the charge storage mode. In this configuration the collector junction acts as the photodiode and the charge storage element by virtue of the collector-to-base capacitance Cc.. The small area, low leakage emitter diode performs the function of a switch. Figure 27 shows a practical structure using a p-n junction as the switch. A schematic representation of a linear array of phototransistors is also shown in Fig. 27. Finally, the linear array can be expanded to form two-dimensional arrays, which are currently under development.20*28 An array of lo4 phototransistors and lo4 MOST’S, with a schematic representation as shown in Fig. 28, uses the additional MOST’s as logic gates for coincident sampling of the phototransistor. When row-column coincidence occurs the MOST is to perform an “AND” function. The array does not require isolation of the individual devices, and therefore eases integration into arrays. The technique of combining storage mode with the MOST logic eliminates the need for sampling a number of output
12.
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503
FIG. 27. Phototransistor operation in the PFI mode. (a) Practical structure using a p-n junction as a switch: and (b) schematic representation of a linear array of phototransistors. (After Weckler.28)
channels, as would be required by simple paralleling of linear arrays. The logic electronics confines the signal current to only one dimension of the sampling systems, thus preventing crosstalk. Only one common signal terminal for all elements of the array is necessary for video signal processing. From the preceding discussion and a comparison with the currentmode operated array as described by Strull et u E . ~ it~ becomes apparent that the two-dimensional phototransistor array with MOST coincidence logic operating in the PFI mode offers the greatest advantage with respect to simplicity of electronics, solid-state fabrication, and sensitivity. 29
M. A. Schuster and G. Strull, I E E E Trans. Electron Den 13,907 (1966).
504
ROBERT SEHR AND RAINER ZULEEF Column
Column
I N
I N+I
Row M t l
,
c
FIG. 28. A schematic representation of the two-dimensional phototransistor array with MOST logic gates for coincidence sampling. (After Dyck and Weckler.zo)
1 3. EXCITATION STORAGE MODE
This sampling mode is a special case of the photon-flux integration which was developed in connection with the thin-film imaging array.” Its primary, but limited, applicability lies with arrays of photoconductive elements where photon flux integration would be possible only by adding shunting capacitors across the photoresistive elements. In the excitation storage mode the effect of the light is stored as excited carriers whose lifetime should approximate the scanning period. Although the effective duty cycle of current flow through each element is only N - ’ times that of an element with full charge storage, this loss in signal can be compensated by using a photoconductor with an internal gain of N electrons per photon. The effective quantum yield of the sensor thus approaches N ( I / N ) = 1, the value equal to the maximum quantum yield expected with photon flux integration. 14. RANDOM ACCESS
Certain applications of imaging devices require variable scan rate or random access to an element or matrix portion. The photon-flux-integration mode is not suitable for such applications, because variation of scan time changes the sensitivity and dynamic range (see Section 12). However, the
12.
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505
photocurrent mode is applicable because the current readout produces a signal proportional to the incident light at the time of interrogation. It is possible then to use variable scan rates or incomplete scans, or to provide random access to the individual matrix elements. This mode is thus more suited for pattern recognition and guidance schemes, where it is not desired to continually scan the entire matrix but rather to concentrate processing on selected areas of the array for certain periods. But the scan rate and sensitivity limit its usefulness (see Section I 1). In high-element-density matrices of more than about 50 x 50 elements the described switching transient limits the frame rate for standard television practice, which provides 63.5-psec time for scanning one line in the U S . television system. V. Imaging Characteristics of Photodetector Arrays
The important parameters describing a photodetector array for imaging are : (1) absolute sensitivity, (2) spectral sensitivity, (3) uniformity of response, (4) resolution, and (5) speed of response. In contrast to individual detector elements, for which such parameters as sensitivity and speed of response are primarily determined by material constants, for detector arrays these values are primarily determined by element structure, element integration, and readout mode. Some of these relations have already been mentioned in the preceding sections. Absolute sensitivity of the imaging array is determined primarily by the device structure (photoconductor, diode, transistor) and by the sampling mode. The combination of phototransistor sampled in the photon flux integration mode provides the highest sensitivity available for electronicallyft-cd. The value of about lo-’ ft-cd scanned imaging devices, about for a similar array sampled in the photocurrent mode is to some extent dependent on phototransistor design and processing because both will influence the limit-setting dark current. Spectral sensitivity in the case of photoconductor arrays is, of course, the same as that of an individual element, and as such is primarily determined by material constants. Ionization energy of the charge carriers, their lifetime, and device geometry are of principal importance. For the diode and transistor, device geometry plays a dominant role. In particular, junction depth and impurity profile variations between devices of the same structure will result in different spectral responses. This effect can be utilized to shift the peak response of pn-junction device arrays. A representative spectral response of a silicon n-p-n transistor within the array is shown in Fig. 29 together with the spectral response (dashed curve) of a silicon junction photodiode. Surface effects caused by planar device fabrication contribute further to the distortion of the “normal” absorption curve. This is especially
506
ROBERT SEHR A N D RAINER ZULEEG
Incident radiation wovelength ( F ) FIG. 29. Spectral sensitivity of a silicon phototransistor in mosaic (continuous curve), and single photodiode (dashed curve). (After Anders et d.")
true for the SiOz passivation film on the silicon surface. Antireflection properties of a quarter-wavelength thick SO, film can produce peak responses at a particular wavelength. Uniforntity qf'response is a very critical performance parameter. It depends on the material homogeneity and processing uniformity. For the sake of a graduated gray scale the response uniformity should be high. A reproduction of a gray scale by a 10 x 10 matrix was shown in Fig. 16. With present silicon planar technology a high degree of uniformity is obtained. A typical response distribution curve of the elements of one matrix is shown in Fig. 30. Minimum and maximum detectable signal levels are approximately 10 nW and 1 mW, respectively. The sensitivity is betwen 10' and lo3 pA/mW. Resolution is determined by the element density of the array. There seems little doubt that silicon will remain indefinitely the dominant material for microelectronics and the fabrication of solid-state imaging systems. The construction of both thin-film and monolithic systems has demonstrated a resolution in excess of 100 lines. Although arrays with resolution inferior
12.
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IMAGING AND DISPLAY
I00 VCE a,
p
e
= 3 volts
95% 80 250 f t
C .VI
c
60
20% of median
E
a,
c
0 a,
m 40 t
c
I A
a,
e
n“
Median
I
20
I
I
0
YL-2 1
40
I
+I 60
3%
I 70
80
90
Photo current (FA)
FIG. 30. Response distribution of elements within a matrix at different light intensities (McDonnell Douglas Corporation).
to broadcast television standards are now practical, one would require an array with approximately 512 x 672 elements to satisfy the tv standards. It is conceivable that both thin-film techniques and planar silicon techniques will eventually reach this goal. A considerable amount of research must be devoted t o the development of matrices with higher element density and sufficient uniformity. Speed ofresponse is related to the particular device and the method of readout. Although the response time of a single phototransistor with an active base area of 4 x 4 mils square is in the range of0.5-1.0 psecs, this speed cannot be realized when the device is incorporated in the multielement matrix (see Section 11). In the photocurrent mode the response time is limited to about 3-5 psec. This time imposes a limitation on the scanning rates of large arrays using this mode of readout. Since, e.g., the time for each television line is approximately 63.4psec, only about 20 elements in one line could be sampled to produce a “low” resolution image. In a high resolution image of 512 x 672 elements only 0.12 psec is allotted for the readout time of the individual element. Sampling times of 0.1-0.2 psec per element are practical for photodiode and phototransistor arrays when operated in the photon flux integration mode (see Section 12). This readout mode therefore leads to all solid-state “high” resolution imaging when a monolithic sensing array with X Y readout is provided with external commutation circuits.
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ROBERT SEHR A N D RAINER ZULEEG
VI. Array and Scanning Circuit Integration The switching speeds necessary to operate large arrays impose severe demands on the response characteristics of the array and on the scanning circuitry. A short readout time is available when the matrix is scanned in the 5-10 MHz frequency range, which would be required, e.g., in application to standard US. television. The mostly capacitative impedances of the interconnects between elements and between matrix and scanning circuitry then become important. To minimize this impedance and thereby allow high scan rates, the detector matrix and the scanning circuitry must be in close proximity so as to allow short interconnects. Several methods have been conceived to achieve this integration. The ideal solution, of course, is the LSI (large scale integration) of the scanning circuitry with the photodetector array on one common substrate. Practical methods so far exercised in the laboratory include separate fabrication of array and scanning circuits and providing connections by thermocompression bonding of hundreds of small gold wires. This can be done on suitable substrates, such as ceramics, with plated and etched large interconnect patterns and joining of the substrates by standard multiterminal miniature connectors. Figure 14 is an example of this method. Another modification, and considerable improvement, would be the bonding of the array and the various scanning and video processing circuitry on one common ceramic substrate and interconnecting the terminals of the closely spaced chips with metal interconnects. Thermocompression bonding seems feasible, but may not be reliable and economical. Other methods for providing these large numbers of small metal interconnects will be sought. If, e.g., the voids between the circuit chips can be filled with some kind of glass or epoxy material which will give a smooth transition between the circuits, then metal interconnects can be deposited either by conventional evaporation through a mask or by evaporation with a laser beam.
VII. Display Devices
A planar, solid-state, optical display panel for viewing by the human eye has been a long-established aim of electrooptical device research. Spurred by the benefits which would result from “flat television receivers,” this goal is receiving continued high attention. Work towards electroluminescent display panels with ac-activated polycrystalline ZnS goes back to the early 1 9 5 0 ’ ~ . ~However, ’ electroluminescent (EL) cells alone do not produce a satisfactory image display for two reasons : First, the electrooptical conversion efficiency of dielectric30
H. K. Henisch, “Electroluminescencc,” pp. 296 ff, 307 ff. Pergarnon Press, Oxford, 1962.
12. IMAGING AND DISPLAY
509
embedded luminescent powders is low, and second, the electroluminescent decay time is very short.Thus a brightness-voltage characteristic results which is insufficient for a high brightness, high contrast display, while the short luminescent lifetime prevents a complete image from persisting for a full frame-time. A further problem, closely related to the inefficiency of dielectricembedded EL powders, lies in the short energizing time for each cell. If there were 100 x 100 cells in the array, each element would have the ac voltage applied for only of a frame time, i.e., for only a small fraction of a cycle. The brightness developed in such a short fraction of a frame time would be minimal. These considerations have led to the development of ferroelectric controlled electroluminescent displays, which are discussed in the following section. With the improvement of crystal growth methods, particularly epitaxial techniques, a new approach to fast switching displays has been taken in the form of diode arrays fabricated from mixed-crystal III-V compounds. Gallium arsenide phosphide, Ga(As - ,PJ and gallium aluminum arsenide, (Ga, -xAl,)As, are currently being investigated. Display panels with epitaxially grown (GaA1)Asdiodes are the subject of Section 16b. 15 . FERROELECTRIC-CONTROLLED ELECTROLUMINESCENT DISPLAY The short electroluminescent decay time and the relatively low brightness of electroluminescent cells require the cell to be energized throughout a frame time. This cannot be done by direct scanning, and so a control device that is capable of rapid switching and of storing video information is associated with each panel cell. A circuit including a ferroelectric capacitor fulfills these basic requirements, and the first EL-ferroelectric panels were described by Sack3’ and by Rajchman and B r i g g ~More . ~ ~ recently Lechner and c o - ~ o r k e r shave ~ ~ developed improved ferroelectrically controlled EL cells and have built large display arrays. The basic ferroelectric control circuit is shown in Fig. 31. Assuming for the moment an ideal ferroelectric (i.e., a ferroelectric having a square hysteresis loop and a threshold electrical field), the circuit operates as follows: If the ferroelectrics F E , and F E 2 are initially poled oppositely, E. A. Sack, Research 12, 54 (1959). J. A. Rajchman and G. R. Briggs, U.S. Patent 3,041,490, June 1962. 3 3 B. J. Lechner, Ferroelectric Electroluminescent Displays, in “Agard Conference Proceedings No. 23-Displays for Command and Control Centers” (I. J. Gableman, ed.), Chap. 25, pp. 35 1-372. Technivision Services (Division of Englehard Hanovia International, Ltd.), Slough, England, 1969; B. J. Lechner, A. G. Samusenko, G. W. Taylor, and J. Tults, Ferroelectric controlled electroluminescent displays, Pror. Nat. Aerospace Electron. Conf., Dayton, Ohio, May 1966.
3’
32
510
ROBERT SEHR AND RAINER ZULEEG
Poled oppositely
Poled ollke
blocked stote
unblocked stote
(0)
(b)
lntermedmte state (C i
FIG.31. Basic ferroelectric control circuit. (After L e ~ h n e r . ' ~ )
they remain in this saturated opposing polarization for either polarity of the field produced by the ac generator A . Hence the ferroelectrics do not switch and no current flows in the circuit (Fig. 31a). If F E I and F E 2 are initially poled alike, they switch in unison when driven by the ac generator, and current flows through the EL cell (Fig. 31b). Switching only over the partial hysteresis loop as illustrated in Fig. 31c produces an intermediate gray level (halftone). Since the initial polarization of FE, determines the switching state of the circuit, the circuit can be set to any intermediate state by applying a voltage between the terminals x and y. Because there is a threshold voltage V, for switching, it is possible to select (or address) a ferroelectric control circuit by coinciding additive voltage swings (coincidence selection). For example, to switch the circuit from the blocked state to the unblocked state a voltage + V is applied to x and - V to y . With V,/2 < V < V, switching will occur only if + V at x and - V at y coincide. Intermediate states are obtained by modulating either the amplitude or the duration of one of the two selection signals. The basic ferroelectric circuit has been designed33 into a display matrix as shown in Fig. 32. The ferroelectric FE3 between point x and the column lines serves as an isolation element. It prevents short-circuiting of the ferroelectric F E , to ground through the internal impedance of the column and row generators Riand C; (i = 1,2,. . .).
12.
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511
FIG.32. Display matrix concept using the basic ferroelectric circuit. (After L e ~ h n e r . ~ ~ )
The less than ideal characteristics of practical ferroelectrics limit the performance of the basic circuit of Figs. 31 and 32 in two ways. First, because ferroelectrics do not have a true threshold, the half-select signals, which address other circuits in the array, gradually unblock a blocked (i.e., a dark) image element. Thus a gradual lighting of supposedly dark elements occurs. However, with the best ferroelectric ~ e r a r n i c s ~presently ~.~ used this effect poses no serious problem. A greater problem is the imperfect squareness of the ferroelectric loop. The latter allows some current to flow in the blocked circuit. The EL cell is thus not completely dark and the contrast is spoiled. With niobium-doped Pb(ZrSnTi)03ferroelectricceramics this effect limits the contrast to about 2 : 1 at brightness levels of 3-4 ft-lm. which circumvents this Lechner has devised a new control shortcoming. The circuit, shown in Fig. 33, consists of two basic circuits 34
35
36
G. W. Taylor, J. Appl. Phys. 38,4697 (1967). C. Wentworth and G. W. Taylor, Am. Ceram. SOC. Bull. 46,1186 (1967). B. J. Lechner, Digest of Technical Papers, 1965 Intern. Solid-state Circuits Conf., Philadelphia, Pennsylvania, 1965; B. J. Lechner, U.S.Patent 3,197,744, July 1965; B. J. Lechner and G. W. Taylor, U.S. Patent 3,393,345, July 1968; B. J. Lechner, U.S. Patent 3,478,224, November 1969.
512
ROBERT SEHR AND RAINER ZULEEG
A
-
A
- Row generator (provides negative pulse)
Center tapped sine wave generator
C - Column generator (provides positive pulse) V B -Back biasfor diode D
FIG.33. Control circuit with center tapped a c generator in
a
bridge arrangement. ( A f t e r
Le~hner.~~)
with center-tapped ac generator in a bridge arrangement and the EL cell connected between the points of balance. The upper ferroelectric pair F E , and F E 2 is always unblocked, whereas the lower pair F E , and FE4 is switched between the blocked and unblocked states. When unblocked, all four ferroelectrics switch in unison, the bridge is balanced, and the EL cell is dark. Instead of relying on the squareness of the hysteresis loop, the current through the EL cell now depends only on the balance of the bridge. When F E , and F E , are blocked the bridge is unbalanced and current flows through the EL cell, causing it to light. The current and hence the brightness depends on the degree to which FE3 and F E , are blocked. Figure 34 shows how the improved circuit is incorporated into a matrix. It differs from the matrix in Fig. 32 in that no reset pulses are required and the ferroelectrics are switched to the blocked state to turn the EL cell on. Display Address Technique Typical switching times of ceramic ferroelectrics are t , = 10psec. This establishes a minimum time for addressing an element or a row of elements. Consider a matrix with i7 rows and m columns which is to be addressed an element at a time. The frame time TFis given by TF = nmt,.
(18)
Allowing guard bands for timing errors, t , is assumed to be 20psec. For a
12.
A1; A2 R1; R 2
C1; Cg; C3
513
IMAGING AND DISPLAY
- Sine wave generators for row 1 and row 2
-
- Row pulse generators for row 1 and row 2 - Column pulse generators for columns 1, 2 and 3
FIG. 34. Incorporation of control circuit of Fig. 33 into a matrix. (After L e ~ h n e r . ~ ~ )
smear-free image TF z 30 msec, so that
nm = TF/ts = 1500 elements.
(19)
Obviously, the resolution for a 1500-element array cannot be high. However, for line-at-a-time addressing TF= nf,, and in this case the array may consist of 1500 rows each consisting of m elements. Thus in this addressing mode large display matrices are possible. In this case a serial-to-parallel conversion must be performed when the video information arrives sequentially in real time as from a vidicon camera. Figure 35 shows a block diagram of a line-addressed 1200-element display with serial video input. The horizontal scanner causes the video signal for one line to be sequentially sampled by the sampling gates. These samples are stored and the information is transferred to the display en mame when the column drivers are simultaneously activated in coincidence with the appropriate row driver. This process is then repeated for successive lines. A 1200-element display matrix33 driven by a vidicon camera is shown in operation in Fig. 36. This display consists of 30 rows of 40 elements, each 0.2 in. sq. The ferroelectric circuits were constructed on 4 in. x $in. x 0.003 in. ceramic strips3’ with 20 circuits on each strip. The device has a
514
ROBERT SEHR AND RAINER ZULEEG
___------__--
Excitation
I
I
I
I
I
I I
L, Vertical scanner Information transfer signal
1 generators
vioeu
Horizontal scanner
-A
FIG. 35. Block diagram of a line addressed 1200-element display with serial video input. (After L e ~ h n e r . ~ ~ )
frame rate of 30/sec and a line addressing time of 40 psec. The 40 elements of each row are sampled ar 20.6-psec intervals. The total horizontal line timeis thus40 x 20.6 psec + 40 psec + 62 psec(f0rguardbands) = 926 psec. This corresponds to a line frequency of 1080 Hz. Scanning signals for the matrix are obtained from clock-driven vertical and horizontal scanners which operate synchronously with the deflection of the electron beam in the vidicon. The maximum “on” brightness which is achieved with a column pulse amplitude of 45 V varies between 11 and 20 ft lm. The average value, plotted in Fig. 37, is 16ftlm, and the upper and lower decile points are 19 and 13 ft lm. For column pulses of 15 V or less all cells have essentially zero brightness. At intermediate halftone settings the variation in brightness is greater. This is by design so as to favor higher brightness at the expense of gradual transfer characteristics.
ELECTROLUMINESCENT DIODE ARRAY 16. SCANNED In contrast to dielectric-embedded powder EL cells, which can only be activated with alternating current and require power densities of several
12.
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FIG.36. The 1200-element model display system in operation. (After L e ~ h n e r . ~ ~ )
hundred watts per centimeter squared, electroluminescence in single-crystal devices can be excited with low voltage, direct current, and with power densities of less than 100 W/cm2. Furthermore, the switching speed, i.e.,
L
M
I_
60
Column pulse amplitude i V )
FIG.37. Averagc value of brightness as function of column pulse amplitude. (After L e ~ h n e r . ~ ~ )
516
ROBERT SEHR AND RAINER ZULEEG
“turn-on time constants,” for electroluminescence in monocrystals is at least an order of magnitude faster than the 1 psec or more for EL panels. In spite of these well-known advantages, monocrystalline display devices are only now on the threshold of reality. The reason for this slow progress is associated with the technological problems of materials preparation. Solid-state displays designed for the human eye as detector require semiconductors with band gaps larger than 1.8 eV. Band gaps of this magnitude are generally associated with melting points in excess of 1400°C and high equilibrium vapor pressures. This is so because the band gap is the result of the bonding forces in the crystal, and these, in turn, determine the temperature at which the crystal melts. The practical problems encountered in the growth of single crystals compound rapidly as the melting point increases, particularly when good single crystals with high purity and controlled doping are required. Silicon carbide and the 11-VI compounds with energy gaps of more than 2 eV and melting points of 1400°C and higher are good examples, in that they have yet to be grown in large, homogeneous, single crystals. An additional difficulty is the formation of a p n junction in these materials. Conventional techniques such as diffusion are not applicable and new methods such as ion implantation have yet to prove successful. Without the ability to make the material into simple p-n junctions, the full benefit of a single-crystal device cannot be realized, since the forward-bias junction is the most efficient radiative structure. A further complication arises from the differentiation between direct and indirect optical transitions associated with the band structure of a particular semiconductor. Wide-band-gap materials with band structure allowing direct optical transitions, and thereby higher electrooptical conversion efficiency, are the exception rather than the rule. When all these considerations are combined they point out the rather narrow restrictions involved, and consequently the small number of semiconductor materials that qualify for use in electrooptical displays, while the majority are presently burdened with problems relating to the band structure or to the materials technology. a. Gallium Phosphide Diodes
Among the more common 111-V compound semiconductors, there are three which on account of their large energy gap would qualify for electroluminescent display applications. These are AIP, AIAs, and Gap. However, all three have indirect optical transition^,^' and the first two have melting
’’ C . Hilsum and A.
C. Rose-lnnes, “Semiconducting Ill-V Compounds,” pp. 33 and 65. Pergamon Press, New York and London, 1961.
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5 1
/ \ Diode P26 298
')c
2 t
-
2
1 Infrared
Red Zn-0 pair band
Greed
c
z
LT
I 12 L " " 14 " " " 16 ' 18 20 22 Photon energy in electron volts
2
FIG. 38. Emission spectrum from a forward-biased Zn-diffused diode at room temperature. (After Gershen~on.~')
points above 1600°C. The third, Gap, with an energy gap of 2.25eV, has been investigated longest and its preparation and device fabrication is best understood. But AIAs, having a gap energy of 2.20 eV, has received much attention lately as a constituent in epitaxially-grown (Gal -,Al,)As (see Section 16b). Pure G a P as well as GaAs-GaP alloy electroluminescent diodes and small arrays of individual diodes are now commercially a~ailable.~'They are primarily used for alphanumerical display." The material is grown epitaxially, either from the vapor phase or by growth from the liquid phase on a GaAs substrate which is subsequently dissolved. Although GaP is an indirect gap semiconductor, its electroluminescent efficiency is high. This is because the emitted light is not due to band-to-band radiative recombination, but originates from two other radiative recombination mechanisms. Figure 38 shows a typical room temperature forward-biased emission spectrum from a diode prepared by zinc diffusion into an n-type crystal containing tellurium and oxygen. Two emission bands appear in the visible, separated spectrally and pa ti ally.^' A weak green band is generated close to the junction boundary, while a much stronger red band originates on the p-side of the junction. The red band has been shown to be due to donoracceptor pair recombination involving shallow zinc acceptors and deep oxygen donor,41while the origin of the green band at room temperature is not quite clear. It may be due to shallow pair recombination or to nitrogen Monsanto Company, St. Louis, Missouri and Hewlett-Packard Company, Palo Alto, California. 39 D. K. Hillman and G. E. Smith, I E E E Spectrum 5,62 (1968). M. Gershenzon, Bell Sysfem Tech. J . 45, 1599 (1966). 4 1 M. Gershenzon, R. A. Logan, and D. F. Nelson, Phys. Rev. 149, 580 (1966). 38
518
ROBERT SEHR AND RAINER ZULEEG
traps which arise from isoelectronic substitution of nitrogen for phosphorus atoms, but band-to-band recombination is ruled out because the observed efficiency is orders of magnitude higher than the indirect gap would allow. Quantum efficiencies for the red and green emission depend upon the junction preparati~n.~’ The external efficiency for red eIectroluminescence was reported to be as high as 1.5 on an alloyed junction made over six years ago. Diodes with efficiencies up to 7 % are being produced today. The green emission is about 100 times less efficient than the red. However, as far as the human eye is concerned, it is the integral of the product of the emission curve and the visual acuity curve that counts. Thus the G a P green emission corresponds to about 650fm/W. For the red band this value is only 20 I m p in spite of the higher efficiency.
x4’
6. Integrated Gallium-Aluminum Arsenide Diode Arrays One of the big problems in the fabrication of diode array displays is the growth of homogeneous large area crystals with uniform junction characteristics. A major advancement in this area has been the solution regrowth first described by Nelson43 for GaAs and later applied to (Gal -,AI,)As for the fabrication of highly efficient electroluminescent diodes.44 Much better uniformity of the Ga-AI ratio can be achieved in this system (variations amount to less than 2% along the growth axis) than in the Ga(As,_,P,) system. The reason is probably the better match in size of the mutually substituting Ga-A1 atoms. The high uniformity of the crystals, the high flatness of the junction, and the virtual elimination of competing deeplying levels45 result in (Ga,-,Al,)As, 0 < x < 0.35, light-emitting diodes with external quantum efficiency of up to 1.2% at current densities of about 50 A/cm’ at 300°K. The switching time for light emission was measured to be 60 n ~ e c . ~ ~ ~ The promising feature of this technique is that junctions with very uniform characteristics can be grown over large substrates. This permits the fabrication of diode arrays in sifu, provided it is possible to have the epitaxial growth occurring only in designated areas or by somehow integrating diode platelets after the growth cycle. The second method is currently being developed46 for the fabrication of visible display panels. The following goals must be aimed at in the design of such panels. 42
H. G. Grimmeiss and H. Koelmans. Phys. Lerters 8, 233 (1964).
‘’ H.Nelson, RCA K e n 24, 603 (1963).
H. Rupprecht, in “Gallium Arsenide”
(Proc. Intrm. Sympositttn, Reading, 1966). p. 57. Inst. Phys. and Phys. SOC., London, 1967. 4s S . M. K u and J . F. Black, J. Appl. Phys. 37,3733 (1966). 45aH.Rupprecht, T. M. Woodall, and G. D. Pettit, Appl. Phys. Letters 11, 81 (1967). 46 H. B. Wetzell, Private communication, March 1968. 44
12.
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Diced GaAeAs
Y-Inputs 1
FIG.39. Perspective view of (Ga, -,AI,)As light emitting diode array. (After W e t ~ e 1 1 . ~ ~ )
(1) The size and diode density of the array should not be limited by the integration technique. (2) Address should be by means of a cross-grid wiring matrix. (3) Heat sinking should be adequate to allow the diodes to be driven to their saturation levels for maximum light output. (4) The fabrication method should lend itself to batch processes. One approach which comes close to meeting these conditions is depicted in Fig. 39. The fabrication of the array starts with metalizations of the grown diode platelets to provide ohmic contact to both the n and p surfaces. The platelets are then cut into regular squares or rectangles as large as the original substrate materials will permit. Next the platelets are bonded to the broad conductive metal strips of an insulating substrate of high thermal conductivity such as boron nitride. The mounted platelets are then diced without cutting through the conducting strips by using masking and etching techniques to form small diode islands. After backfilling the grooves and thus providing a smooth surface a second set of conducting strips is applied to the top of the diode array, perpendicular to the bottom strips in order to form a cross-grid pattern for X-Y scanning of the array. The final operation consists of etching into the diode islands to expose the emitting junctions. The diameter of the etched holes should be as large as possible for several reasons : (1) the remaining p-n layer surrounding the holes will be small, resulting in high current density for low driving currents ;
520
ROBERT SEHR AND RAINER ZULEEG
TABLE I COMPARISON OF DISPLAY CHARACTERISTICS' ~
Electrical optical characteristics
EL panel
Incandescent lamp
Brightness (ft Im) Life (hr) Voltage (V) Current ImA) Speed Color
8 400 ll5ac 1 1 psec White
500 10,Ooo 4.5 72 1 msec White
_ _ _ _ ~
Gas discharge
GaP diode
90
200
2000
40,000 2 dc 20 100 nsec Green-red
160 ac 0.2 85psec Neon-red
GaAlAs diode
1000 >40,000 2 dc 15 60 nsec Red
~
"After W et ~ e1 1 . ~ ~
(2) more junction area is exposed for maximum light output ; and (3) less nonradiating surface remains, rendering the display more continuous. By filling the cavities with a glass or epoxy of high index of refraction the external quantum efficiency can be further increased. With present microelectronic techniques it appears possible to fabricate diode arrays with up to 100diodes/in. Proper heat sinking provided, (GaA1)As diodes have exhibited brightness levels of 150 ft lm. Depending on ambient light conditions, six to eight points on the gray scale have been estimated using Hardy's criteria.47 In Table I the principal parameters of various display devices are summarized. As can be seen from the values given, the diode display appears the most promising approach with the proviso that a large scale integration technique can be perfected.
VIII. Parallel Readout Image Converters The three principal domains of imaging are (1) the viewing of inaccessible or distant scenes, (2) the direct viewing of scenes at very low light levels (image intensifier), and (3) the direct viewing of scenes at spectral illuminations different from the visible, particularly in the infrared (image converter). In this classification the scanned devices discussed in Sections 2 and 3 are most applicable either for distant imaging or for nonvisible imaging, while very low light level viewing, below ft-c, is presently the exclusjve domain of photoemissive tube devices. The following discussion pertains 47
A. C. Hardy, Rept. E 1385, Instrumentation Lab., M.I.T., Cambridge, Massachusetts, July 1963.
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521
only to converters with response times that permit the imaging of a moving picture.
17. NONREGENERATIVE IMAGECONVERTERS For the direct viewing of nonvisible images planar image converters have been developed which contain a radiation-sensitive layer and an electrooptical display layer sandwiched together with the necessary electrodes. The display layer is generally a polycrystalline electroluminescent (EL) material, while the radiation sensitive layer may be a photoconductor (PC) sensitive to x-rays, ultraviolet, visible light, and infrared, or it*may be an infrared sensitive element such as a thermistor array. Although not very efficient with respect to energy conversion, these polycrystalline devices have the outstanding feature that they can be made in large panels (up to 20 x 20 in.) and thus provide pictures on a one-to-one scale. The basic structure of a solid-state image converter is shown in Fig. 40a. The EL-PC layers are usually applied to a glass substrate, which provides the mechanical support. The optical isolation layer between the radiationsensitive input layer and the EL output layer prevents undesirable optical feedback between the two. The equivalent electrical circuit of the converter Transparent electrode Electroluminescent layer Optcol isolation layer Radiation sensitive layer Transparent electrode Glass substrate
(a 1
Resolution element
*
RPC
REL
(bl
FIG.40. Solid-state image converter. (a) Basic structure: and (b) equivalent circuit.
522
ROBERT SEHR AND RAINER ZULEEG
panel is shown in Fig. 40b. Each image spot or resolution element is a series combination of photoconductor impedance Z,, and electroluminescent impedance Z E L , each of which has a resistive component RPc and RE,, respectively, and a capacitive one, Xpc and XEL,respectively. The operation of the device rests upon the radiation controlled variations of impedance Zpc in the photoconductor layer, which causes a corresponding increase or decrease of voltage drop across the electroluminescent layer, intensifying or reducing its light emission proportionally. This voltage divider action of the PC-EL pair provides a nonregenerative amplification function which depends on the relative impedance of the PC and EL layers. It is quite obvious that RE, represents a parasitic path across the electroluminescent EL layer, and should therefore be much larger than XEL:
The fact that this condition is poorly met in most electroluminescent materials is the reason for their low energy conversion efficiency. With a loss tan 6 x 0.01 the electrooptical conversion efficiency is of the order of 1%.48
For the PC input layer it is a basic requirement that the opticallycontrolled impedance range embrace the impedance of the EL layer. But since the radiation-induced impedance changes are resistive only, because the radiation has no effect on X,, this requirement can be stated in the form RLi < X,, < R g ) ,
(21)
where L stands for illuminated and D for dark. A primary performance characteristic of an image converter is the ratio of photons emitted by the EL layer to photons incident on the PC layer. A measure of the photon output is the brightness BE,,which is related49 to the applied voltage V,, by
BE, = uf” exp( - kV;2/2),
(22)
where f is the excitation frequency and n a constant (0.5 Q n < l), and u and k are constants relating to the maximum brightness. Keeping in mind conditions (20),the applied voltage V,, can simply be expressed in terms of the PC-EL impedances and the excitation voltage V, (see Fig. 40) by
48
49
G. F. .I.Garlick, Aduan. Elecfron. Electroll Phys. 16, 607 (1962). G . Diemer and J. G. Van Santen, Philips Res. Rept. 15, 368 (1Y60).
12.
523
IMAGING AND DISPLAY
10
1 +
a 3 c
3
1
0.1
001 Io
I0-'0
-~
10-8
I6 '
10-6
Photoconductivity FIG.41. Effect of photoconductor capacitance on EL output. (After Stewart.5o)
For V,, > 10 V Eq. (22) can then be expanded in the form BE, = @{I
-
k[i(
1
+% XE,
RPC RPC f X P C
)I1"}.
(24)
From Eq. (24) it can easily be shown5' that high efficiency and high contrast ratio require50a that X,, 9 XEL.If this condition is not fulfilled, the shunting impedance X,, limits the voltage swing across the EL layer and thereby reduces the light output. Figure 41 shows how the minimum brightness of the EL output layer depends on the capacitive and resistive component of the P C input layer. No matter how efficient the resistive component is, the contrast ratio of the EL layer is limited by the PC capacitance. In order to realize extremely small PC capacitance, Stewart5' has used a special electrode structure, shown in Fig. 42. The radiation enters the photoconductor layer through the windows in the common electrode. The type of construction affords good optical absorption efficiency, since none of the radiation is lost to absorption or reflection from a transparent electrode. Moreover, radiation entering at an oblique angle and passing twice through the photoconductor is reflected back into the bulk of the PC layer. This has the effect of broadening the spectral response by extending the shortwavelength cutoff. The spectral response with a CdSe photoconductor is shown in Fig. 43. The 20 x 20 element array is fabricated on a 0.007-0.009-in.-thick glass substrate. The apertures in the common electrode are 0.04in. in diameter 5 0 R. D. Stewart, I E E E Trans. Electron Deu. 15, 220 (1968). ""The expression equivalent to Eq. (24), as given by Stewart," erroneously contains a factor ek and neglects a factor k in front of the inner bracket.
524
ROBERT SEHR AND RAWER ZULEEG Top view of PC electrodes (not to scale)
la) Side view of PC-EL converter (not to scale)
Common electrode Continuous photoconductor CdSe Opaque dielectric Individual electrodes Electroluminescent layer TransDarent electrode EL light output
(b)
FIG.42. Structure of photoconductor-electroluminescent converter. (After S t e ~ a r t . ~ ' )
on 0.05-in. centers. The diameter of the individual electrodes on the opposite side of the 0.002-in.-thick photoconductor is 0.02 in. The calculated capacitance Cpc of this structure is 1.25 x 10-I4F, and the ratio of the capacitance of the 40-mil-diam EL element C,, to Cpc is 2900. This is almost two orders of magnitude larger than a parallel-plane structure of the same dimensions would yield. The overall operating efficiency of the image intensifier is essentially that of the EL material alone: 7-12 I m p . The entire 20 x 20 array dissipates 15 mW/in.2 at 200 V. 18. PSEUDOREGENERATIVE IMAGECONVERTER
The most important operating parameters of an image converter are sensitivity, response time, and transfer function. While sensitivity and response time are predominantly determined by the photoconductor
12.
525
IMAGING AND DISPLAY
10
\A I0,OOO
12. 00
FIG.43. Spectral response of a CdSe photoconductor. (After Stewart.”)
material and the applied voltage, the transfer function in the general form
which relates the light output of the device, in lumens per unit area, to the light input, is a complex function of both materials, the PC and EL layers, as well as the device structure, the operating voltage V, and frequency w. The exponent y in Eq. (25) is generally taken to describe the transfer function Lo,, with the understanding that it refers to the center portion of the transfer curve. Since gamma determines the slope of the curve (in a double-log plot), it can be interpreted as the gain of the device. Two examples of transfer curves were shown in Figs. 4 and 41. For a given PC-EL combination and device structure there usually exists an optimum operating voltage and frequency which establishes the y, or gain, of the converter. A three-terminal converter developed by Kohashi et al.” differs remarkably in this respect. Not only can the gain vary over a wide range, but it can also be inverted, i.e., y can vary within a range of positive and negative values. When operating the converter with a negative y the original, positive image incident on the PC layer is emitted as a negative image from the EL layer. Areas that were originally dark are emitted light, and vice versa.
’’ T. Kohashi, T. Nakamura, H. Maeda, and K. Miyadi, Aduan. Electron. Electron Phys. 22B, 683 (1966).
526
ROBERT SEHR AND RAINER ZULEEG
lo2
I
Light input (arbitrary units)
FIG. 44. Different transfer functions obtainable with thc image-converter panel. (After Kohashi et d s ' )
The change of imaging mode is accomplished by applying two ac driving potentials with the same frequency and varying the phase and amplitude relation between the two. The different transfer functions obtainable with the converter are shown in Fig. 44. Curves A , B, and C correspond to positive image transfer of standard, low, and high y and contrast ratio, respectively, curves E and F to negative image transfer of large and small y and contrast ratio, respectively. Curve C represents an intermediate image transfer function between positive and negative, i.e., a V-shaped characteristic which is obtained for a certain phase and amplitude relation between the two driving potentials. A cross section through the three-terminal converter together with a schematic representation of operating conditions is shown in Fig. 45. This converter is composed of three principal layers.
(1) A photoconductive layer about 80 p thick of CdSe powder is bonded with epoxy resin. Incorporated with the layer is a parallel fine grid electrode of 10-p-diam tungsten wire and 0.6 x 0.6 mm grid dimension. (2) An electroluminescent layer of ZnS powder about 50 p thick is bonded with epoxy resin onto a transparent electrode of SnO, on a glass plate. (3) There is a transparent dielectric layer between the photoconductor layer and the second transparent SnO, electrode. Between the photoconductor and the electroluminescent layers is an optical antifeedback layer consisting of an opaque layer and a reflective BaTiO, layer.
12.
527
IMAGING AND DISPLAY
Glass plate Transparent electrode Transparent dielectric layer Fine grid electrode PC layer (CdSe) Opaque layer BaTiO3 reflecting layer Electroluminescent layer (ZnS) Transparent electrode 1,
FIG. 45. Cross section of three-terminal converter together with a schematic presentation of operating conditions. (After Kohashi et ~ 2 1 . ~ ' )
The converter is operated by applying two ac potentials V, and V, of the same frequency but of differing phase, as illustrated in Fig. 45. Here II is the lateral photocurrent due to the voltage V, and the light input intensity Li, and I , is the capacitive current associated with V,. The current that flows through the electroluminescent layer is the vector sum l 3 of the currents I , and I,. Light output Lo from the EL layer is nonlinear and increases rapidly with the amplitude of current 1 3 . The current I , is an incremental function of V,, while I , is an incremental function of V, and the incident light level Li . Therefore by adjusting the amplitude and phase relationships of the potentials V, and V,, the amplitude of Z3,and thereby the electroluminescent light output L o , becomes an incremental, decremental, or V-shaped function of Li. Since the variation of gain and output image polarity is reminiscent of an amplifier with a regenerative feedback loop of variable gain, the term pseudoregenerative converter is used. A photograph of test pictures for a positive, a V-shaped, and a negative image emitted from a 20 x 20cm EL layer is shown in Fig. 46. As can be seen, white areas in the positive image (a) are black in the negative image (c) and gray in the V-shaped image (c). The measured image resolution was greater than 800 lines with static input images. For a moving picture the resolution increases. The response time (risetime) of the converter is of the order of lOmsec, but is strongly dependent on illumination level. Nevertheless the device is
528
ROBERT SEHR AND RAWER ZULEEG
FIG.46. Output images of image converter panel in various modes of operation. Output images for: (a) positive, (b) V-shaped, and (c) negative characteristics. (After Kohashi et nLsl).
capable of reproducing flicker-free moving images. This quality, combined with the negative image transfer function, makes it ideally suited as a motion picture film editing device. ACKNOWLEDGMENT Thanks are due to 9. J . Lechner for his helpful comments on the section concerned with display devices.
Author Index Numbers in parentheses are footnote numbers and are inserted to enable the reader to locate thosecross referenceswhere theauthor’snamedoes not appear at the point of reference in the text. A Abraham, A., 30,33,41(27) Abrams. R . L., 285,383 Abnkosov, N.Kh., 187,188,190(19) Albers, W., 114,I40 Allgaier, R. S., 129 Almasi, G. S., 186,252 Alper, T., 187,188,190(20) Anders, R. A., 489,490(18),506 Anderson, L. K., 374,412 Anderson, R.L., 85 Andrews, J. C., 273,278(17) AntonEik, E., 30 Arams, F., 346,349(31), 353(31), 405,409,422 Armstrong, J. A., 373 Arnold, R. T., 260 Ashley, K. L.,89 Astheimer, R. W., 273,285,303,313 Attard, A. E., 33(32), 34(32), 35, 36(32),
43(32), 47(32), 49(32), 54 Avery, D. G., 16,17,46,63(4) Ayache, J. C., 203,204(52), 217,218 Ayas, A,, 407 Ayas, J., 199,204(36), 242,245(36), 246(36),
250
B Bahr, A. J., 373 Bailly, F., 186,203(12), 236,237(83), 238,252 Baird, J. R., 89 Bardeen, J., 167 Bardsley, W., 127 Barrie, R.,19, 20(17) Bartlett, B. E., 46,68,234 Baruch, P.,95 Bass, J. C., 436 Bates, R.L., 302 Beattie, A. R.,215
529
Bebb, H. B., 343 Beerman, H. P., 260,279(10), 285 Behle, A. F., 490,497(21) Bell, E. E., 336 Bennett, H.E., 29,31 Bernard, W.. 418 Betts, D. B., 303 Black, J. F., 518 Blair, J., 182, 183, 187, 190(3), 234,241(3),
243 Blakemore, J. S . , 31,215,217(71), 478 Blatt, F. J., 167 Bloembergen, N., 372 Blue, M.D., 199,202,203,214 Blunt, R. F., 17,63 Boltaks, B. I., 138,139(31) Born, M., 377 Bostick, H. A., 346,365,400,401,402,403 Boulton, J. S., 127 Bozorth, R. M., 454 Brand, F. A., 436 Bratt, P., 5 , 12(2) Braunstein, R.,89,90 Brebrick, R. F., 129,137,138,140,186 Bridges, T.J., 404 Briggs, G. R., 509 Brown, R. N., 200 Bube, R. H., 226 Buck, T.M., 475,476(10), 477(10) Buckley, R. E., 273 Buczek, C. J., 346,375,383,405,426,427,428 Bullis, W.M., 26,27(19), 28(19) Burdick, G. A., 260 Burgess, R. E., 223,355 Burstein, E.,336
Butler,J.F.,112,113,114(8),116(9),117,123, 126,127,138,159,383,389 Bylander, E. G., 112
530
AUTHOR INDEX C
Cadoff, 1. B., 288.293,297,298 Cady, W. G., 259 Calawa,A.R., 112,113, 114, 115(16),116(16), 118(16), 119(16), 120, 121, 140, 141, 143, 151(12), 157, 383, 389 Callahan, D. E., 489,490(18), 506(18) Cardona, M., 192, 193(28), 195, 198, 199, 200(39), 201(28),254(28) Carlson, R. O., 187, 190(16) Chang, T. Y.. 404 Chantry, G . ,275 Chao, P. Y., 490, 497(21) Chapin, D. M., 454 Chapman, R. A., 343 Chasrnar, R. P., 187, 287, 294(15), 297(17), 301(25), 308(34), 309(35) Cheo, P. K.,404 Cholet, P., 16 Choo, S . C., 39, 48(35), 54(35) Chynoweth, A. G., 260 Coates, D. G . , 154, 165(39) Cohen-Solal, G . , 186. 203, 204(53), 236, 237, 238,252 Coleman, P. D., 363. 374(14), 404,410,414(7) Conklin, J . B., Jr., 112 Cooper, J., 260, 272(7), 273(7), 278(7) Cope, A. D., 473 Corcoran, V. J . , 373 Corrigan, F. R., 298 Crowell, M. H., 475. 476, 477 Cruceanu, E., 187 Cuff,K. F., 159, 169 Cummins. H. Z., 364, 365 Cunnell, F. A., 18 Cunningham, R. W., 26,27,28
DeVore, H. B., 40 Dexter, R. N., 202, 210 Diament, P., 371 Dickey, D. H., 189, 190(24), 195, 199, 201(31, 32), 204(31. 32), 210(31) DiDomenico, M.. Jr., 346. 363, 374, 375(13), 404, 410, 414(7), 429(6) Diemer, G . , 522 Dimmock. J. O., 112, 113(1), 114, 151(12), l57( 13), 383,384, 389,480,481,482 Di Nardo, A,, 422 Dirac, P. A. M., 370 Doyle, W. M.. 382 Dresselhaus, M. S., 199, 201(31, 32), 204(31, 32), 210(31) Duley, W. W., 281 Durham, E. W., 187 Dyck, R. H., 490, 502(20), 504 Dziuba, E. Z . , 189, 190(25),202, 234
E Eddolls, D. V., 436, 438 Eden, R. C., 363, 374(14) Egli, P. H.. 288, 298 Ehrenreich, H., 30, 31(24) Eisenman, W. L., 302 Ellen, P. C., 234 Ellett, M. R., 159, 169(42) Ernmons, R. B., 346,362,363,374(12),375(13), 404(12, 13) Engler. W., 5, 12(2) Esaki, L., 112, 1 l3(5) Evans, R. D., 398
F D Dacus, E. N., 289 Dalton, J. V., 475, 476(10), 477(10) Davenport, W. B., Jr., 397, 398(62d) Davies, T. J., 63, 64(57) Davisson, J . W., 336 Deans, J., 234 Decque, J., 204, 250(54) DeHaan, E. F.,474 DeNobel, D., 184 Desse, M . , 95 DeVaux, L. H., 16. 17, 63(4)
Fan, H. Y., 28, 29, 35, 36, 39, 40, 47, 49(33), 453, 454, 456(10) Fedorova, N. N., 95 Fink, D. G., 469 Finn, M., 114, 115(16), 116(16), 118(16), 119(16), 120(16), 121(16), 140(16), 141(16), l43( 16) Flood, W. F., Jr., 29, 32(22) Folberth, 0. G., 95, 104 Foreman, J. W., Jr., 365 Forrester, A. T., 346, 361, 364(1), 372(1), 390 Foss, N. A,, 240
531
AUTHOR INDEX
Fourge, S. V., 469,473, 476(6) Fournier, G., 468 Fourny, J., 204, 250(54) Frederikse. H. P. R., 17, 63 Freed, C., 353, 373, 389, 397, 398 Fried, D. L., 364 Friis, H. T., 431
G Galavanov, V. V., 39 Galazka, R. R., 188, 190(20a), 202, 204. 212, 243(59) Galginaitis, S., 187, 190(15) Garbuny, M., 415 Garfunkel, J. H., 203 Garlick, G. F. J., 522 Gatchell, E. K . 102, 436, 440(2), 446(2), 447, 448(2), 452(2), 463(2) Gavrishchak, 1. V., 204, 210 Gebbie, H. A., 285, 362 Gebel, R. K . H., 478 Ceiling, L., 308 George, E. W., 365 Gerber, W.D., 382 Gershenzon, M . , 517. 518(40) Gibson, A. F., 30 Giriat, W., 201 Glass, A . M., 285, 383 Glauber, R. J., 366, 367, 368(25, 30), 369(25), 370, 371(25), 389(24), 396 Glicksman, M., 455 Gobeli, G. W., 28, 29 Goldberg, A . E., 16 Goldsmid, H. J., 292 Goodman, J. W., 400 Goodrich, R. R., 469, 473, 476(6) Goodwin, D. W., 16, 17, 46, 47, 49(49), 50 Goodwin, F. E., 363, 374(15) Goryunova, N . A., 95 Could, G., 376, 377(51), 396(51), 400 Granger, R., 199, 204(34), 241(34), 242, 250, 25 1 Gray, P. E., 292, 293 Grimmeiss, H. G., 518 Groves, S. H., 195, 197,200 Grube, R. H., 325,326(5) Griin, K. 114 Gubner, E., 140
Gudmundsen, R. A., 361, 364(1), 372(1) Gulyaeva, A. S., 38, 39 Gunn, J . B., 451
H Haas, C., 114, 140 Hadni, A , , 260,279(11), 285, 298 Hall, L. H., 167 Halsted, R. E., 189, 190(26) Hanlon, J., 374 Hansen, J.. 415 Hardy, A. C., 520 Harman, T. C., 63,113, 114,1I5,116(9,16). 117, 118(16), 119(16), 120(16), 121(16), 123, 126, 127, 135, 140(16), 141(16}, 143(16), 151(12), 157(13), 159(27), 164(18), 165,183,190,195, 199, 201, 204, 210, 212, 234, 254. 353, 383, 389,397 Harned, B.. 346, 362, 374(12), 404(12) Harp, E. E., 26, 27(19), 28(19) Harris, L., 289, 298 Harris, S. E., 346,361,362,363(2), 372(2), 409 Haseltine, W. A., 365 Haus, H. A,, 373. 389 Havens, R. J., 301 Hawkins, T.D. F., 30, 31(25) Haynes, J. R., 446 Heasell, E. L., 39, 48(35), 54(35) Henisch, H. K . , 508 Henninger, Y . , 260, 279(11) Henoc, J., 186 Henry, P. S. H., 130, 138(26), 139(26) Herman, F., 112 Herschel, W., 287 Hicinbothem, W. A,, Jr., 455 Hill, D. E., 89 Hillman, D. K., 517 Hilsum, C., 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 516 Hinkley, E. D., 353, 397, 398 Hobden, M. V., 89 Hollis, J. E. L.,39, 48, 54 Holter, M. R., 294 Honig, J. M., 135, 159(27), 195 Hornbeck, J. A., 446 Howarth, D. J., 19, 20(17) Hrostowski, H. J., 29, 32 Hulme, K. F., 18, 20, 21, 63, 64 Hurle, D. T. J., 127
532
AUTHOR INDEX
I Iglitsyn, M. I., 38(37), 39 Ioffe, A. F., 298 Ivanov-Ornskii, V. I., 189, 190(25), 197, 203, 204(4Y)
Ivleva, V. S., 38(37), 39
J
Jackson, J. K., 302 Jacobs, H., 436 Jacobs, S. F., 346, 361, 362(5), 363(5), 364(3), 366, 369(3, 3, 372(3, 5), 374, 376, 377(51), 396(51), 400(51), 409 Jarnieson, J. A., 325, 326 Jaumot, F. E., 292, 294(12) Jensen, J. D., 154 Jetton, J. L., 365 Johnson, K. M., 335 Johnson, L. E., 112 Johnson, P. 0..361, 364(1), 372(1) Jones, F. E., 287, 294(15), 297(17), 301(25), 308(34), 309(35) Jones, R. C., 4, 267,301,325, 314,464 Jones, R. H.. 19, 20(17)
K Kallen, D., I14 Kamadjief, P., 203, 204(53) Kane, E. 0.. 18,253 Kaye, S., 85 Kelemen, F., 187 Kent, M. J., 30 Kesamanly, F. P., 197 Keyes, R. J., 346, 348(29), 375, 381(49), 383(49), 405,422
Kimmitt, M . F., 30, 261, 273(15). 278 King, R. E. J., 46, 68, 493 Kingston, R. H., 346, 348(29), 375, 381(49), 383(49), 422
Kiuchi, Y.,473 Kleinman, D. A., 87, 88 Kleiner, W. H., 195 Knable, N., 364 Knibb, T. F., 436 Koelmans, H., 518 Koga, M., 260, 279( 13)
Kohashi, T., 525, 526, 527, 528 Kolesar, D. F., 188, 189, 190(21) Kolm, H., 353 Kolomiets, B. T., 197, 203, 204(47, 49) Koster, W., 95 Kot, M. V., 203,204 Kraus, H., 240 Krebs, H., 114 Kremenchugskii, L. S., 260, 279(12) Kroeger, R. D., 376, 396(52) Kruse, P. W., 5, 17, 39, 40, 43, 53, 65, 68, 69, 70, 203, 204, 205(58), 210, 218, 221(74), 225(74), 232(74), 234, 246, 252, 301
Ku, S. M., 518 Kudman, l., 89 Kuglin, C. D., 159, 169(42) Kurnick, S. W., 16, 17, 30, 31(26), 39, 63(4), 453
L Labuda, E. F., 475,476(10), 477(10) Ladd, L. S., 187, 190(18) Laff, R. A,, 35, 36, 39,40,47,49(33), 453,454, 456(10)
Landsberg, P. T., 215 Lang, S. B., 260 Lange, R.,422 Lasser, M . E., 16,346,361,362,369(4), 372(4), 374( I2), 404( 12) LaTourette, J. T., 376, 377(51), 396(51), 400(51)
Lawson, J. L. 331 Lawson, W. D., 17, 63(4), 154, 165(39), 203, 204
Lebloch, H., 249, 250(94), 252(94) Lechner, B.J.. 509,510,511,512,513,514,515 Leiba, E., 285, 383 Lennard, J. K., 77, 78, 79. 80, 82 Levinstein, H., 5, 6, 12(2). 374 Lewis, R. D., 365 Lewis, W. B., 325 Liang, S. C., 63 Limperis, T..329 Lipson, H., 336 List, W. F., 487,489,490(18), 497(17), 506(18) Logan, R. A., 517 Long, D., 19, 28(16), 41, 170, 177, 181, 182, 190(1), 191, 192(1), 193(1), 194, 195, 196, 197(1), 198,199,200(37), 201(1),208,209(64), 210(64), 214, 222, 226, 233(1), 330, 356
533
AUTHOR INDEX
Lopez, A., 85 Lorenz, M. R., 189, 190(26) Lorimor, 0. G., 189, 190(23) Lucke, W. H., 292 Lucovsky, G., 346, 362, 363, 374(12), 375(13), 404 Ludeke, R., 240 Ludlow, J. H., 260, 261,273(15), 276, 278(15)
M McCann, D. H., 489,490(18), 506(18) McDermott, P. S., 235 McFee, R. H., 325, 326(5) McGlauchlin, L. D., 5, 39, 40(39), 43(44), 53(52), 65(58), 68(61), 69(6J, 62), 70(61), 218, 221(74), 225(74), 232(74), 301 McMurtry, B. J., 346, 361, 362, 363(2), 372(2), 409,412 McQuistan, R. B., 5,39,40(39), 43(44), 53(52), 65(58). 68(61), 69(61, 62), 70(61), 218, 221(74), 225(74), 232(74), 301 MacRae, A. U., 5, 12 McSkimin, H. G., 188, 190(22) Madelung, O., 18 Maeda, H., 525, 526(51), 527(51), 528(51) Mali, M., 204 Mal’kova, A. A,, 197, 203, 204(47, 49) Mal’nev, A. F., 260, 279(12) Mandel, L., 346, 361, 364(6), 369, 370, 371, 390 Marfaing, Y.,186, 203, 204(52, 53), 217, 218, 236, 237(83), 238, 249, 250(94), 252 Markov, Yu.,199 Maronchuk, Yu. Y., 203, 204(46) Martienssen, W., 397 Martinuzzi, S., 204, 250(54) Massey, G. A., 376 Matreev, 0. V., 116 Mavroides, J. G., 188, 189, I90(21, 24), 195, 199, 201(31, 32), 204(31, 32), 210(31) Medved, D. B., 85, 100, lOl(25) Mekhtiev, A. Sh., 197 Melloni, M., 287 Melngailis, I., 112, 113, 114, 115, 151(12), 157(13), 159, 164(18), 165, 199, 204, 236, 238(87), 241(35), 383, 384, 389,405 Meray-Horvath, L., 494, 495(27), 496(27), 497(27), 504(27) Merrian, J. D., 302
Meyer, J. E., Jr., 494,495(27), 496(27), 497(27), 504(27) Mezrich, J. J., 373 Miller, E., 288, 293, 297, 298 Mitchell, G. R., 16 Mitchell, W. H., 260, 276(14) Miyadi, K., 525, 526(51), 527(51), 528(51) Mocker, H., 383 Moore, C. B., 365,415 Morten, F. D., 493 Moss, T. S., 17, 18, 30, 31(25), 40, 46,63(4) Mshenskii, V. A., 203,204(46) Mullin, J. B., 63, 64 N Nakamura, T., 525, 526(51), 527(51), 528(51) Nasledov, D. N., 37, 39, 54 Neda, A,, 187 Nelson, D. A., 187 Nelson, D. F., 517 Nelson, H., 89, 90(8), 518 Neuringer, L. J., 418 Newnham, R., 182, 183, 187, 190(3), 234, 241(3), 243 Newstein, M., 376, 377(51), 396(51), 400(51) Nicolosi, S. J., 16, 17, 63(4) Niculescu, D., 187, 202 Niculescu, N., 202 Nielsen, S., 203, 204(44) Nikolic, P. M., 112 Nipkow, P., 469 Nobel, P. J. W., 490 Norr, M. K., 123, 153(23) Novikova, S. I., 187, 188, 190(19) Novoselova, A. V., 116 Nudelman, S., 294
0 Ober, H., 114 Oliver, B. M., 373, 409 Oswald, F., 103
P Pace, F., 346, 349(31), 353(31), 405,422 Pankove, J. I., 89,90(8) Pantell, R. H., 346, 363, 375(13), 404, 410, 414(7)
534
AUTHOR INDEX
Parker, S. G., 240 Patel, C. K . N., 410 Paul, W., 195, 197, 240 Pauling. L., 96 Pedinoff, M. E., 363, 374(15) Pehek, J., 5, 12(2) Peretti, E. A,, 95 Pershan, P.S., 372 Petersen, P. E., 215 Petritz, R. L., 145, 227, 404 Pettit. G. D., 518 Peyton, B., 346, 349(31), 353(31), 405,422 Pihnn, W. G., 87 Pfleegor, R. L., 370, 371 Phelan, R. J., 480, 481, 482 Philipp. H. R., 30, 31(24) Picus, C;.S., 346, 375, 383,405,415,426, 427, 428 Pidgeon, C. R., 200 Pike, W. S., 494, 495(27), 496(27), 497(27), 504(27) Plass, G. N., 325, 326(5), 328 Powell, J. M., 30. 31(26) Powers, J . K., 346, 362, 374(12), 404(12) Prdtt, G. W., Jr., 112 Prince, M. B., 87 Prior, A. C., 116, 154, 165(39) Pruett, G . R., 145. 227, 404 Psoda. M., 188, 190(20a) Putley. E. H., 19, 20(17). 203, 204(44), 260, 261, 273( 15). 276( 14). 278( 1 9 , 285, 362
Q Quarrington, J. E., 19, 28, 30
R Rabinowitz, P., 346, 361, 362(5), 363(5). 366. 369(5), 372(5), 374(5), 376,377(51), 396(51), 400(51), 409 Rajchman, J . A,, 509 Ray, B., 182, 183,234, 243(2) Read, W. T., 35,41,48 Rediker, R. H., 151 Redington, R. W., 438, 478, 479, 480 Reese, W. E., 89 Rennie, A. E., 16, 17(2), 46 Richards, R. G., 325, 326(5) Rignoux, P.,468
Rittner, E. S., 41, 166. 167(43) Roberts, V., 19, 28, 30. Rodot, H., 186, 204 Rodot, M., 204,236,237(83), 238,249,250(94), 252(94) Roess, L. C., 289 Rolik, C i . P., 100, lOl(25) Root, W. L., 397. 398(62d) Rose, A., 335, 436, 437, 438(3, 4) Rose-Innes, A. C., 18, 19, 20, 21, 22, 23, 24, 25, 516 Ross, I. M.. 17 Ross, M., 346 Rupprecht, H., 518 Ruthroff, C. L., 404 Ryder. E. J., 451 S Sack. E. A,. 509 Sadasiv, G.. 494. 495(27). 496(27), 497(27), 504(27) Sdker, E. W., 18 Samoilov, V. V., 260, 279(12) Samusenko, A. G., 509, 510(33), 513(33) Sard, E., 346, 349(31), 353(31), 405 Saunders, G. A,, 187, 188, 190(20) Saur, W. D., 200, 203 Sawyer, D. E., 151 Scanlon, W.W., 137 Schampers, P. M., 474 Schlickman, J. J., 253 Schmit, J. L., 183, 184, 185, 186,200,201(39b), 204, 205(58), 206, 207(63), 249, 253(39b) Schmitz, W. D., 46 Schneider, W. E., 302 Schodder. G. R., 114 Schoolar. R. B., 154 Schuster, M. A., 487, 497(17), 503 Schwartz, R. F., 363, 375(13), 404(13) Schwarz, F., 285 Scott, M. W., 200,201(39a), 203(39a). 214(39a), 253(39a) Sella, C., 236,238(85) Segall, B., 189, 190(26) Seidel, T.. 89 Seraphin, B. O., 29, 31 Shaunfield, W. N., 458 Shaw, N ., 260,276( 14), 285,362 Shih, C., 95 Shimazu, M., 273, 278(19)
535
AUTHOR INDEX
Shimizu, K., 473 Shneider, A. D., 203, 204, 210 Shockley, W., 35, 41, 48, 147, 167, 214 Siegman, A. E., 346, 347, 361, 362, 363(2), 364, 367,372(2), 373( 16), 376. 377(16), 409 Simashkevich, A. V., 203, 204(46) Skillman, S., 1 I2 Skripkin, V. A., 197 Slack, G. A., 187, 190(15) Smetannikovd, Yu. S., 37, 39, 54 Smith, A. C., 186,252 Smith, A. W., 373 Smith, B. A., 95 Smith, G. E., 517 Smith, J. P.. 240 Smith, R. A., 287, 294, 297, 301, 308. 309 Smith, S. D., 30, 31(25) Smith, W., 468 Smollett, M., 177, 217(la) Sniadower, L., 188. 189, 190 (20a, 25) Sommers, H. S., Jr., 102, 436, 437, 438(5), 440(2), 446(2,5), 447,448(2), 452(2), 463( 2,5) Soref, R. A,, 415,484,485, 491,492 Sosnowski, L., 202, 204,212 Speer, H., 490, 497(21) Speerschneider, C. J., 183, 184, 185, 186, 240 Spencer, P. M., 183 Spenke, E., 150 Spiller, E., 397 Spitzer, C. R., 273 Spitzer, W. G., 189, 190(23) Stafsudd, O., 304 Stair, R., 302 Stanford, A . L., Jr., 260, 279(8) Steckel, F., 260 Stelzer, E. L., 200, 201(39h), 236, 238, 239, 240(82), 253(39b) Stephenson, J. C., 365 Stevens, N., 304 Stewart, R. D., 523, 524, 525 Stierwalt, D., 106 Stiles, P. J., 112, 113(5) Stocker, H. J., 63 Stone, N . W. B., 285, 362 Strauss, A. J., 16, 17,33(32), 34(32), 35,36(32), 43(32), 47(32), 49(32), 54,63(4), 112, I13(1), 114, 120, 151(14), 186, 195, 199, 201, 204, 210(31), 212,241(35), 254,383,384,453 Strozyk, J. W., 436 Strull, G., 503
Stuckes, A. D., 187 Sturge, M. D., 89 Suda, K., 260, 279(13) Suits, G. H., 46, 294 Sun, C., 457 Suzaki, Y., 273, 278(19) Svelto, O., 346, 363, 375(13), 404,410,414(7), 429(6)
T Ta, Yeou., 260 Takami, K., 260, 273, 278(19), 279(13) Takatsuji, M., 273, 278(19) Tauc, J., 30, 33, 41 Taylor, G. W., 509, 510(33), 511, 513(33, 35) Teich, M. C., 346, 348, 362, 364, 365, 366, 367(23), 369(23), 370(23), 371,372(7),373(23), 375, 376, 377, 378, 379, 380, 381(49), 382, 383, 385, 386, 387, 388, 389, 390, 392, 395, 399,406,422 Terhune, R. W., 46 Teutsch, W. B., 437, 438(5), 446(5), 463(5) Thoma, B., 95 Thomas, D. G., 188, 190(22) Thomas, R., 260,279(11) Thomson, S. P., 288 Thornton, J. R., 365 Titulaer, U. M., 367, 368(30), 370 Torrey, H. C., 41 I , 420(8) Townes, C. H., 362, 363, 373 Tufte, 0. N., 212, 236, 238, 239. 240 Tults, J., 509, 510(33), 513(33) Turner, W. J., 89, 336 Tyler, W. W., 337, 338(13), 339 Tyrziu, V. G., 203, 204(46)
U Uhlenhech, G. E., 331 V
Van Der Drift, A., 474 van der Ziel, A,, 147, 374, 405(47) van Heerden. P. J.. 478,479,480 van Roosbroeck, W.. 87, 167,214 Van Santen, J. G., 522 Van Vliet, K. M., 5, 41, 50, 221, 223, 224(75), 230(75), 374, 404(44), 412
536
AUTHOR INDEX
Vergnat, P., 260,279( 1 1) Verie, C., 199,204,206,207(38), 212,241(34), 242, 245(36), 246(36), 249, 250, 251, 252, 407 Vieland, L., 89 Vink, H. J., 140 Vogl, T., 415 Volkov, A. S., 39
W Wagner, J. W., 115 Walsh, E. J., 475, 476(10), 477(10) Walsh, T. E., 457 Wang, M., 409 Washwell, E. R., 169 Wasscher, J. D., 114 Watanabe, S. H., 490,497(21) Waters, W. R., 302 Watson, H. J., 365 Weaver, J. N.. 346, 363, 374( 14), 375(13), 404( 13)
Weckler, G. P., 490, 499, 500, 501, 502, 503, 504
Weimer, P. K., 469, 476(6), 494, 495, 496, 497(27), 504(27)
Weiner, S., 303, 313 Weiss, H., 18, 93, 95 Weitz, S.. 436 Welker, H ., 15, 18, 93 Wendland, P. H., 476 Wentworth, C., 51 , 513(35) Wertheim, G. K., 5, 54 Wetzell, H. B., 518, 519, 520 Wheatley, G. H., 29, 32(22) White, D. J., 280 White, M. B., 382 Whitmer, C. A,, 411, 420(8) Whitsett, C. R., 187 Wiley, J. D., 202, 210
f
Willardson, R. K., 115 Williams, D. B., 66, 67, 69, 77, 80, 81, 82, 83 Williams, L. R., 159, 169(42) Williams, R. L., 226, 438, 458 Wing, M. E., 489, 490(18), S06(18) Wolf, E., 369, 377 Wolf, M., 87 Wolfe, W. L., 294 Wolga, G. J., 366, 371 Wood, A. D., 273, 278(17) Woodall, T. M., 518 Woodbury, H. H., 337. 338(13), 339 Woolley, J. C.. 95, 182, 183, 234, 243(2) Wright, G. B., 195, 199, 201(31), 204(31), 210(31)
Wright, H. C., 436, 438 Wurst, E. C., Jr., 16 Wyncke, B., 260, 27% 11)
Y Yardley, J. T., 415 Yariv, A,, 426 Yates. H., 328 Yeh, Y., 364, 365 Young, A. S., 203,204(44) Youtz, P., 114, 115(16), 116(16), 118(16), 119(16), 120(16), 121(16), 140(16), 141(16), 143( 16)
Z Zakrzewski, T., 204 Zemel, 3. N., 154 Zhmurko, I. S., 203 Zissis, G. J., 294 Zitter, R. N., 17, 31, 33, 34, 35, 36, 39, 40, 41, 43,47,49(32), 54, 57,63(4), 453
Zlomanov, V. P., 116 Zworykin, V. K., 469
Subject Index B
A Absorption coefficient AlSb, 93 direct gap semiconductors, 86 GaAs, 90-93 GaSb, 93 Ge, 93 Hg,-,Cd,Te, 202-204 InSb, 27-29, 93 InAs, 93 InP, 93 Pb,-,Sn,Te, 335 Si, 93 Activation energies, see Impurity activation energies Aluminum antimonide (AISb), absorption coefficient, 93 Ambipolar diffusion length, 40 magnetic field, 58 Analytic signal, 369, see also Coherent detection Annealing PbSn chalcogenides, 118, 128-137, 142-144 two-zone, 136, 137, 143, 144 Antimony oxide (Sb,O,), 473 photoresponse, 473 resistivity, 473 Arrays, 336 Atmospheric window, 365 Auger effect Hg,-,Cd,Te, 2 14-2 17 InSb, 30, 47 theory, 215, 216
Background-limited infrared photoconductor, 12, 41, 53, 225, 227, 322, 326, 342, see also BLIP Band inversion, 112 Band structure CdTe, 194 HgTe, 195-199 InSb, 191 nonparabolic bands, 192-194 Pb,-,Sn,Se, 112-114 Pb,-,Sn,Te, 112-1 14 Beamed-scanned imaging devices IR vidicon, 477-480 Au-doped Si, 478-480 quantum efficiency, 480 laser-scanned MOS device, 4 8 0 4 8 2 Plumbicon, 474, 475 Sicon, 474-477 collection efficiency, 477 Vidicon, 470-473 CdSe target, 473 charge storage mode, 472 Sb,S, target, 473 Bias, see also Detector bias power effect on g-r noise, 418, 419 on mixer gain, 414, 422-425 voltage effect on carrier concentration, 426428 on frequency response, 422-425 on mixer gain, 411, 422-425 on mobility, 426-428 on resistivity, 426-428
537
538
SUBJECT INDEX
Black body emittance. 323, 324 Black body temperature, 7 standardization, 4 BLIP, 12, 41, 53, 225, 227, 322, 326, 342, see also Background-limited infrared photoconductor Bridgman technique Pb,.,Sn,Se, 119-128 Pb,,Sn,Te, 119-128 Broad band systems, see also MBPD microwave bias, 438, 439 performance factors, 446-448 frequency response, 446 quantum efficiency, 446 retrieval efficiency, 446-448 sensitivity, 446-448 signal-to-noise ratio, 447 Burstein-Moss effect, 233 C
Cadmium selenide (CdSe), 473, 526 conductivity, 473 spectral response, 525 Cadmium telluride (CdTe), 178, 183 band structure, 194-196 dielectric constant, 190 effective masses, 195, 196 elastic constants, 188-1 90 energy gap, 178, 194, 195 melting temperature, 184, 185 thermal conductivity, 187 thermal expansion coefficient, 187 Calcium difluoride (CaF,) attenuators, 380, 385 Carrier injection, see Injection Carrier lifetime, 437 Hg ,$d,Te, 2 13-2 18 InSb, 31-39 Cavity figure of merit, 440 parameter, 440, 442, 464 reentrant, 439-443 resonant frequency, 442 Cellular growth, 126 Characterization, infrared detectors, 3-12 C0,-N,-He Laser, heterodyne measurements, 375-377 Coherence first order, 367, 370, 373, 389
higher order, 389, 390 spatial, 367, 377 Coherence time, 381,397 Coherent radiation detection, 345-359, 361ff, see also Heterodyne detection, Homodyne detection, Photomixing analytic signal, 369 atmospheric distortion, 364 classical theory, 371, 372 conversion gain, 363 counting rate, 369 directivity, 364 frequency selectivity, 364 linearity, 364 optimum sinusoidal mixing, 397 photoconductors, 363 photodiodes, 362 photoemissive devices, 362 quantum theory, 365-371 return from steam, 403 semiclassical theory, 365-372, 396 signal-to-noise ratio, 372, 380-389 submillimeter region, 362 three-frequency configuration, 407 tracking of truck, 401, 402 Compensation, doped Ge, 426-428, see also Germanium (doped) Constitutional supercooling, 126-128 Contacts capacitive, 436 Hg,_,Cd,Te, 246 ohmic, limitations, 437 ohmic, minority carrier sweepout, 437 Conversion gain, see also Heterodyne detection, Mixing current-voltage characteristic, 420, 432-434 design criteria, 414, 429,430 effect of dark conductance, 434 methods of measurement, 421 variation with IF frequency, 411, 422425 with mixer parameters, 41 I , 424 Correlation function coherent detection, 366 second order, 389 Crystal evaluation, Hg,_,Cd,Te crystal perfection, 244 density, 242, 243
539
SUBJECT INDEX electron-beam microprobe, 243, 244 stoichiometry, 244 Crystal growth, see Preparation techniques
D D*, 4, 6, 7, see also Detectivity, normalized, L): InSb arrays, 493 pyroelectric detector, 270 radiation thermopiles, 301, 3 11 Si monolithic arrays, 492 thermal detectors, 8, 301 D 9, 43, 328, 332-336, see also D*, Spectral detectivity diode detector, 146-148, 159 Ge:Hg, 333 InSb detectors, 72, 75, 76 intrinsic versus impurity PC, 335 PbSn chakogenides, 138-162, 169-171 Pb,_,Sn,Te, 333 PC mode, 224-226 Hgl-,Cd,Te, 226, 227 PV mode, 231, 232 Hg,_,Cd,Te, 232, 233 Density operator, radiation field, 367, 370, 371 Depolarizing factor, 440, 444-446 Detectivity, 4, see also D* background noise-limited, 225, 23 1, 232 detectas PbSn chalcogenide, 154-1 58 photoconductive, 224-226 photovoltaic, 145-148, 23 I, 232 g-r noise-limited, 225, 226 hSb, 40 Johnson noise-limited, 224, 225 normalized, 4, see also D* particular wavelength, 6, see also D* A pyroelectric detector, 270 p-n junction, reverse biased, 374 shot noise-limited, 232 spectral, definition, 224 Detector bias, see also Bias microwave, photoconductive detector, 436 Detector design, 39, 40
c,
Detector theory photoconductive mode, 219-227 photovoltaic mode, 227-233 Diffuse reflector heterodyning, 389-400 focused case, 392 radar case, 394 target motion, 394 unfocused case, 393 narrow band random process, 394 power spectral density, 389-392 Diffusion Hg,_,Cd,Te, 186, 187 P b ,_,Sn,Se, 137- 143 Diode detectors, see also Photovoltaic detectors detectivity, 146-148 efficiency, 148, 149 l/f noise, 146 fabrication, 151-153 injection current, 145 I-V characteristic, 160 Johnson noise, 146, 147 quantum efficiency, 145, 155 saturation current density, 147 shot noise, 147 voltage responsivity, 146 Direct gap semiconductors, 18, see also Energy gap absorption coefficient, 86 NBSFD, 92 Display, 467ff, see also Imaging Display devices, 508-520, see also EL (electroluminescent) displays Doppler shift, 364, see also Heterodyne detection heterodyne measurements, 375 Doppler velocimeter, 365, see also Heterodyne detection
E Effective mass CdTe, 196 Hg,_,Cd,Te, 201 HgTe, 196, 197 Pb,-,Sn,Te, 159 ZnTe, 196 EL (electroluminescent) displays, 508520
540
SUBJECT INDEX
EL (electroluminescent) displays (cont.) comparison of characteristics, 520 EL panel, 520 Ga,_,Al& diode, 520 GaP diode, 520 gas discharge, 520 incandescent lamp, 520 ferroelectric control, 509-512 switching times, 512 scanned diode arrays, 514-520 Ga,-,AI,As, 5 18, 520 GaAs,_,P,, 517, 520 Gap, 516-518 Elastic constants CdTe, 189, 190 HgTe, 188-190 Electrical conductivity, see specific materials Electroluminescence, Hg,-,Cd,Te, 204 Electron-beam microprobe, 238, 240, 243-244 Electronically scanned photodetector arrays, see also Photodetector arrays doped detectors Ge, 483 Si, 484 film detectors, 484 InSb elements, 493 D*, 493 LSI, 508 monolithic structures D*,492 quantum efficiency, 492 response time, 492 Si doped, 490 undoped, 487 planar technology photodiodes, 484,485 transistors, 484, 485 quantum efficiency, 486 phototransistors, 486 Si diodes, 486 structures, 483-492 thin film arrays, 493-496 Electrooptical imaging, see Imaging Energy conversion devices, 87 Energy gap CdTe, 195, 196 common semiconductors, 176, 177
Kg ,-,Cd,Te, 198-200 HgTe, 195-197
InSb, 176, 191 Pb,_,Sn,Se, 112-1 14 Pb,.,Sn,Te, 112-1 14 wavelength units, 176 Environmental radiation, see Radiation, environmental Extinction coefficient, InSb, 29-3 1 Extrinsic detectors, 9
F l/f Noise, 5, see also Noise diode detector, 146 PbSn chalcogenide detectors, 170 Fabrication diodes, lead-tin chalcogenide, 151-154 heterodyne detector, 35 1-353 heat sinking, 352 Hg,-,Cd,Te contacts, 246 element preparation, 245 encapsulation, 246-248 surface treatment, 246 windows, 248 InSb, 62-70 MBPD, 444,445 PC detector, 62-70 PEM detector, 62-70 pyroelectric detector, 273-276 Field of view, 326, 327, 464 Frequency response broad band detectors design criteria, 41 1, 413, 414 improved (via compensated materials), 415, 421, 426 measurement technique, 41 5-419, 42 1 microwave, 415-419, 421, 422 roll-over frequency, 421 variation with bias voltage, 426-428 InSb detectors, 73-75 photoconductors versus photodiodes, 404
G g-r Noise, 5 , 40-42, 328-331, see also Generation recombination noise, Noise background flux, 328, 399
541
SUBJECT INDEX
cavity wall photon flux, 328-330, 334 Ge:Cu, 374 heterodyne local oscillator, 347-349, 374 InSb, 50 mixer, 412-419 PbSn chalcogenide detectors, 170 P C mode, 221-224 signal flux, 328, 329 thermal, 330, 344, 355-358 impurity photoconductor, 330, 357 intrinsic photoconductor, 330, 357, 3 58 Gain, photoconductive, 440 frequency dependence, 440 saturation, 437 Gain-bandwidth product, 436438,464 improving cavity parameter, 464 limit, 438 Ga,AI,_,As, 518 GaAs,P,-,, 251 Gallium antimonide (GaSb), absorption coefficient, 93 Gallium arsenide (GaAs) absorption coefficient, 90-93 NBSFD, 87,94 Gallium phosphide (Gap), 516 Gaussian random process, 396-398 Generation recombination noise, 5, 40, 41, see also Noise, g-r Noise InSb, 50 Germanium absorption, 93 detectors, 9 doped compensated (for high-frequency response), 415,426-428 (3-doped, 336340, 342-345 compensated, 415, 418,419 frequency response, 35 heterodyne detection, 348-353, 374-382,415-419,422-425 noise modulation, 38 1 photoconductor gain, 382, 383 detectors D * , 11 D: (Hg-doped), 333 Hg-doped, 178, 334, 336, 426 MBPD, 457, 458
heterodyne detection, 375, 383, 415 solubility of Cu, 339 MBPD, 450452,459, 461-463 Golay cells, 8 Graded-gap structures, 252
H Hall coefficient, see specific materials Hanbury-Brown-Twiss effect, 371,397 Havens limit thermal detector, 301, 302 Heat sinking heterodyne detector, 352 Heterodyne detection, 321-359, 409ff, see also Coherent radiation detection, Homodyne detection, Photomixing basic equations, 346-350 circuit, 347 conversion gain, 363 detector characteristics, 378-389 Cu:Ge, 379-383 detector fabrication Ge:Cu, 378,379 Pb,_,Sn,Se, 383-3 87 Pb,-,Sn,Te, 389 Doppler shift, 364 Ge:Cu, 346,421425 GHz response, 354,415-419,422-425 Golay cells, 362 Hg,-,Cd,Te junctions, 354, 355 high-frequency detection, 354, 415419, 422-425 InAs diode, 363, 374 InSb diodes, 354, 362 LO power, 352,353 mixer, see Mixing NEP, 412 noise, 347-349 Pb,-,Sn,Te junctions, 354 photoconductors compared to photodiodes, 403-406 device responsivity, 405 frequency response, 404 signal-to-noise ratio, 403, 404 temperature of operation, 405 photovoltaic detectors, 171 power detection limit photoconductor, 348 photoemitter (reverse p-n junction), 348 pyroelectric detector, 362
542
SUBJECT INDEX
Heterodyne detection ( f o n t . ) quantum noise limited, 421, 423 receiver analyses, 429-43 4 10.6 micron, 421-426 sensitivity, 412 shot noise, 373 signal-to-noise ratio, 348 thin-film Pb,_,Sn,Te, 355 Heterodyne detection (diffuse reflector), see Diffuse reflector Heterodyne receiver (sensor) configuration, 363, 364 detector fabrication, 351-353 measured characteristics, 422-426 noise, 424 Heterodyne signal amplitude fluctuations, 398 envelope, 396-400 probability density, 396-400 “higher-order” properties, 407 noise, 347-349 power-spectral-density, 382, 391-396 line width, 398 Lorentzian shape, 398 Heterodyne spectroscopy, 364, 391 Homodyne detection, see also Heterodyne detection hornodyne action, 439
I Iconoscope. 469 IF amplifier effective noise temperature, mismatched conditions, 43 1 noise, 412, 419-421, 429 signal-to-noise ratio, 430 wide-band, 419-421 applications, 415 IF signal GHz bandwidth, 409ff heterodyne receiver, 347-349 Image converters, 520-528 nonregenerative, 52 1-524 pseudoregenerative, 524-528 Image intensifiers, see Image converters Imaging, 467ff, see also Display, Imaging devices history, 468-470
parameters, 505-507 absolute sensitivity, 505 resolution, 506, 507 response speed of, 507 uniformity of, 506, 507 spectral sensitivity, 505, 506 readout methods, see Photodetector arrays, Readout methods solid state, 468, 470 spectral region, 468 Imaging devices, see also Imaging beam scanned, 470-482, see also Beam scanned imaging devices electronically scanned, 483-496, see also Electronically scanned photodetector arrays Impact ionization, InSb. 30 Impurity activation energies, InSb, 21 Incoherent radiation detection, low level, 322-345 Indium antimonide (InSb) absorption coefficient, 27-30, 32, 93 band structure, 191 carrier lifetime, 18, 31-39, 43, 47, 48, 54 carrier mobilities, 18, 20, 23-25, 28 conductivity, 22 effective mass ratio, 28 energygap, 15, 16, 18, 19, 176, 191, 493 extinction coefficient, 29-3 I g-r noise, 40-42, 50, 51, 55-57 Ge doping, 20, 2 1, 26-28, 29 Hall coefficient, 20, 22, 26, 27 impurity activation energies, 20, 21 internal photoeffect, 33 intrinsic carrier concentration, 19, 20, 44 intrinsic detectors, 11 magnetoresistance, 26, 59, 60 MBPD, 453-456, 459, 460 NBSFD, 94 nonparabolic bands, 18, 192, 193 quantum efficiency, 30, 33 recombination, 3 1-39,41-43, 48-50, 58,59 refractive index, 29-3 1 resistivity, 21, 22, 25, 44 spectral response, 10
543
SUBJECT INDEX Indium antimonide (InSb) detectors, 10, see also Indium antimonide detectivity, 10, 18, 72, 73, 75, 76, 493 performance data, 70-83 statistical distribution, 77-83 photoconductive, 15-83 photoelectromagnetic, 15-83 responsivity, 18, 45 Indium arsenide (InAs) absorption coefficient, 93, 94 detectors, 10 heterodyne detection, 363, 374 MBPD, 453, 459-462 NBSFD, 94 Indium arsenide phosphide (In,As,-,P), NBSFD, 87 Indium phosphide (InP), absorption coefficient, 93 Information retrieval efficiency, see Retrieval efficiency Injection, majority carrier, 437 Interference, photon, 370 Internal photoeffect, InSb, 30 Intrinsic carrier concentration, see afso specific materials Hg,_,Cd,Te, 253-255 Intrinsic detectors, 10 spectral response, 10 Intrinsic photoexcitation, InSb, 30 Irradiance, 42 1
Johnson noise, 5, 40, 331, 334, see also Noise, thermal diode detector, 146, 147 mixer, 4 12,429 PC mode, 222 PV mode, 231 pyroelectric detector, 268, 284, 285
K k p theory, 192-198, 203, 204, 253-255 Kelvin relation, 288, 292 KMER, see Kodak Metal Etch Resist Kodak Metal Etch Resist, 67 Kodak Photoresist, 67 KPR, see Kodak Photoresist
L Laser emission Hg,-,Cd,Te, 204 Pb,_,Sn,Te, 397 quantum phase fluctuations, 398 Laser radar, 365 Lead oxide (PbO), 474 Lead selenide (PbSe), detectors, 9 D : , 10 Lead sulfide ( P b S ) , detectors, 9 D : , 10 Lead telluride (PbTe), detectors, 9 Lead-tin chalcogenide detectors, 111-174, see also Pb,_,Sn,Se, Pb,Jn,Te Lead-tin selenide (Pb,_,Sn,Se) annealing, 118, 128-137 band structure, 112 carrier concentration, 115, 116, 122, 135-137 carrier mobility, 115, 116, 122 detectivity, 158-162 detectors, temperature of operation, 405 diode, I-V characteristic, 385 energy gap, 113, 177 heterodyne detection, 375, 378, 383388, 415 noise modulation, 389 ohmic contacts, 152 phase diagram, 121 response speed, 161-163 responsivity, 154-158, 384, 406 Lead-tin telluride (Pb,_,Sn,Te) absorption coefficient, 335 annealing, 118, 128-137 band structure, 112 carrier concentration, 115, 116, 122, 131-134, 161, 163, 171 carrier mobility, 115, 116, 122, 171 detectivity, 158-162, 333 detectors, 10 temperature of operation, 405 diode, I-V characteristic, 160 effective mass, 159 energy gap, 113, 161, 177,201 heterodyne detector, 355, 384, 389, 415 ohmic contacts, 152 phase diagram, 121, 126 properties, 334
544
SUBJECT INDEX
Lead tin telluride (Pbl-,Sn,Te) (cont.) response speed, 161, 162 responsivity, 157, 158, 165 Lead zirconium tin titanium oxide (Pb(ZrSnTi)O,), 51 1 Lifetime bulk, 167 hole, Ge:Cu, 344 PC, 166 radiative recombination, 167 reduction, 337 Li,SO,*H,O, pyroelectric detectors, 260, 284 LO (local oscillator), 347-349, see also Heterodyne detection effect, mixer resistance, 414-416, 422425 lasers, 364 noise, 386 power, 352, 386, 421, 422 photoconductor gain, 382, 383 LSI (large scale integration), photodetector arrays, 508
M Magnetoreflectivity, Hg,-,Cd,Te, 204 MBPC, 435ff, see Microwave-biased photoconductor detector Mercury cadmium telluride (Hg,_,Cd,Te) absorption coefficient, 202-204 alloy-composition determination, 240, 242-244 Auger recombination, 216, 217 Brillouin zone, 181, 182 carrier lifetime, 213-21 8 conduction band structure, 192 conductivity, 204-212 crystal evaluation, 242-244 crystal growth, 234-241, 251, 252 crystal perfection, 244 crystal preparation, 233-242 crystal structure, 180-182 cyclotron resonance, 201, 204 density, 182, 183, 242, 243 detectivity, 226, 227, 23 1-233 detector characteristics PC, 249, 250 PV, 250, 251 detector fabrication, 244-248
detectors, temperature of operation, 405 dielectric constant, 190 diffusion, 186, 187, 235-242 effective mass electrons, 193, 201, 202, 204, 217 holes, 180, 193, 21 1, 217 elastic constants, 188-190 electrical contacts, 245, 246 electrical properties, 204-212 electrolurninescence, 204 energy band structure, 189-202 gap versus temperature, 200, 201, 249, 250 general discussion, 177-180 graded-gap devices, 245, 252 Hall coefficient, 186, 204-212, 241 Hall mobility, 204, 209-213 heterodyne detection, 383, 415 impurities, 186, 212, 213, 252 interdiffusion, 186 intrinsic carrier concentration, 206208, 253-255 laser, 204 lattice constant, 182, 183 lattice properties, 180-1 89 lifetime, excess carrier, 213-218, 222, 252 magnetoreflectivity, 204 MBPD, 456,457 mobility electrons, 206-210 holes, 211-213 noise, generation-recombination, 222 optical absorption, 198, 200, 202, 203, 214 optical phonon energies, 190 p-n junctions, 204, 227ff, 241, 242, 250, 251 PC, 203 response time, 226 PEM effects, 204 phase diagram, 183-186, 241 photoconductive mode, 219-227 photoconductivity, intrinsic, 200, 203, 204,217, 249, 250 photoelectromagnetic effect, 204, 217 photoluminescence, 204 photovoltaic detectors, 179, 250, 251 photovoltaic effects, 198, 204, 241, 250, 251
545
SUBJECT INDEX
photovoltaic mode, 227-233 physical parameters, 187-190 purification, 233, 234, 252 radiation recombination, 214, 21 5 recombination, 213-218 stoichiometric defects, 213 thermal conductivity, 187, 190 thermal expansion, 187, 188, 190 Mercury cadmium telluride (Hg,-,Cd,Te) detectors, 10, 175-225, see also Mercury cadimum telluride Mercury sulfide (HgS), impurities, 212 Mercury telluride (HgTe), 178, 183 band structure, 195-199 dielectric constant, 190 effective masses, 196-198 elastic constants, 188-190 energy gap versus temperature, 200 impurities, 212, 213 magnetooptical effects, 200 “negative” energy gap, 178, 195-198 optical absorption, 202,203 thermal conductivity, 187 thermal expansion coefficient, 187, 188 Mercury zinc telluride (Hg,-,Zn,Te), 199 crystal growth, 233 energy band parameters vs composition, 202 lattice constant vs composition, 182 thermal conductivity, 187 Microwave-biased photoconductor detector, 435ff versus dc bias, 436 extrinsic PC, 436 intrinsic PC, 436 measured response Ge, 450-452 Ge(Hg-doped), 457, 458 Hg,,Cd,Te, 456, 457 InAs, 453 InSb, 453-456 Si epitaxial film, 448, 449 single crystal, 448, 449 microwave equivalent circuit, 439, 440 noise reduction, 4 6 2 4 6 4 optics, 445 angle of field, 445 conical light pipe, 445 numerical aperature, 445
performance factors frequency response, 446 retrieval efficiency, 446-448 sensitivity, 446-448 signal-to-noise ratio, 447 reentrant cavity, 439, see also Cavity reflection cavity, 439 sample mounting, 444 shot noise limit, 447 variable coupling, 442, 443 Minimum detectable power, 7, 332-336 heterodyne detection, 373 photoconductor (extrinsic), 375 photovoltaic diode, 375 Minority carrier sweepout, 437 Mixer resistance dark, 415, 416 effect on mixer gain, 425 photoexcited, 414, 415 variation with bias voltage, 428 with carrier lifetime, 414 with carrier mobility, 414 with temperature, 421 Mixing, 410, see also Mixer resistance, Photomixing bias power, 41 7-4 19 bias voltage, 41 I, 426, 427 conversion gain, 410, 41 1, 414, 420, 421, 430, 433 dark conductance, 434 frequency response, 415-417 heterodyne detectors, basic equations, 346-3 50 I-V characteristics, 420 performance analysis, 432-434 NEP, 421 mixer, 421 noise, 410, 412-419 output resistance, 414, 415 performance, 410,420-422, 432-434 photoconductive, design equations, 410-415 response measurement, 415-419 wide-band applications, detector materials, 415 Multiphoton processes, 370
N Narrowband detectors, 349 NBSFD, 85
546
SUBJECT INDEX
Narrowband self-filtering detectors, 85108, see also NBSFD binary 111-Vmaterials, 94 fabrication, 89, 98, 102-105 field-of-view, 99, 105, 106 GaAs materials, 98-102 InAs,P,, materials, 102-106 performance data, GaAs devices, 106108 quantum efficiency, 101, 102, 106 reverse bias tuning, 100, 101 signal-to-noise data, 102, 106 spectral response, 99, 100, 105 ternary 111-Vmaterials, 94-97 tuning techniques compositional, 93 junction depth, 94 reverse biasing, 94 temperature, 93 NBSFD, 85-108, see also Narrowband self-filtering detectors NEP, 3, 4, see also Noise equivalent power Nipkow disc, 469 Noise amplifier, 268, 412, 429, see also IF amplifier background, 225, 227, 231, 232, 323325 “excess,” heterodyne detection, 373 l/f, 5, 40, 146, 222, 328 g-r, 5, 40, 41, 42, 50, 221-224, 328330, 412, 415419,429 heterodyne receivers, 347-349, 424 InSb detectors, 40, 41, 56 Johnson, 5, 40, 146, 147, 221, 222, 331, 412, 429, see also Noise, thermal MBPD, 462-464, see also Signal-tonoise ratio PC mode, 221-224 photon, 5, 53, 325, 326, 328 photon induced, 41 PV mode, 230, 231 pyroelectric detector, 266-271 quantum, heterodyne receiver, 409, 410,412-414 radiation, 267
shot, 147, 230,231, 374 photodiode (reverse biased), 373 photoemitter, 373 spatial inhomogeneities, 325 filtering techniques, 325 temperature, 5, 267 thermal, 40, 42, 50, 429 InSb photoconductors, 46 preamplifier, 347-349 Noise equivalent power, 3, 4, 326-328, see also NEP, RNEP diode detector, 146 Ge:Cu, 342, 343 heterodyne receiver, 412, 423-425 10.6 micron design tradeoffs, 412,414,429-430 effect of IF amplifier, 412,424, 426 variation with mixer parameters, 412, 423-425 pyroelectric detector, 268-272 Noise modulation bandwidth, 381, 382, 389 Noise spectra, InSb detectors, 73-77 0
Optical absorption coefficient, see Absorption coefficient InSb, 27,29, 30 Optical communication receivers, 460463 Optical transmission, ZnSb, 32 P p-n Junction detector, 86-92, see also
Photovoltaic detector reverse-biased detectivity, 374 RNEP, 374 P-representation, 370, 396 PC detectors, see also Photoconductive detectors basic circuitry, 219 g-r noise, 42, 222-224 InSb, 15-17,41-57 preparation, 62-70 minimum detectable power, 375 mixers, 410-419 signal-to-noise ratio, 375 thermal noise, 42
SUBJECT INDEX
Peltier coefficient, 290, 291 PEM detectors, 15-17, 176, 252, see also Photoelectromagnetic detectors InSb, 15-17,57-76 preparation, 62-70 Performance data, see also specific materials InSb-PC detectors, 70-83 InSb-PEM detectors, 70-83 pyroelectric detector, 276-282 thermal detectors bulk materials thermopiles, 305-307 evaporated thermopile arrays, 3 12317 thin film devices, 307-3 11 Phase diagram Pb,-,Sn,Se system, 121 Pb,,Sn,Te system, 121, 126 Pb-Te system, 114, 115 Photoconductive current, short-circuit mode, 41 Photoconductive detectors, 15-17, 176 see also PC detectors g-r noise, 42, 374 heterodyne detection, 374, 375 InSb, 15-17,41-57 preparation, 62-70 PbSn chalcogenides, 163-171 carrier lifetime, 166-168 detectivity, 169-171 responsivity, 164-166, 169-171 microwave bias, 436, see also MBPD thermal noise, 42 Photoconductive response time, 41 Photoconductivity, 8, 176, 436 Hg,-,Cd,Te, 203, 217 Photocurren t collection efficiency, 477 decay time Sicon, 476 Vidicon, 476 diode, 486, 500 Plumbicon, 474 Sicon, 475 transistor, 486, 500 wavelength response, 478 Photodectector array, 483, see also Electronically scanned photodetector arrays
547
characteristics absolute sensitivity, 505 integration, 508 resolution, 506 response speed of, 507 uniformity of,506 spectral sensitivity, 505 monolithic structures, 487 silicon doped, 490 undoped, 487 narrow-gap semiconductors, 493 photosensitive structures, 483 photoconductor element, 483 photodiode, 485 phototransistor, 485, 490 thin-film structures, 493 Photodiode current, 486, 500 versus MBPD, 436 quantum efficiency, 486 reverse biased, heterodyne detection, 373 structure, 485 Photoelectromagnetic effect, see also PEM detectors Hg,_,Cd,Te, 204, 217 InSb, 15-17, 57-76 Photoemitter, heterodyne detection, 373 Photomixing, 377, see also Heterodyne detection, Mixing optimum, 377, 406 sinusoidal, optimum, 370 three-frequency, 407 Photon counting condition for, 446 versus heterodyne detection, 362 Photon detectors, 8 detectivities, 12 time constants, 12 Photon noise, 5, 325, 326, 328, see also Noise Phototransistor, 485, 487, 497 current gain, 486 response time, 498, 501 Photovoltaic detectors, see also Diode detector, p-n Junction detector basic configuration, 228 carrier lifetime, 172-174
548
SUBJECT INDEX
Photovoltaic detectors (cont.) detectivity, 145-148 efficiency, 148, 149, 171, 172 fabrication, 151-153 Hg,_,Cd,Te, 204 InSb, 16, I7 junction capacitance, 150 minimum detectable power, 375 NBSFD, 85-108 quantum efficiency, 87-92 response speed, 149-151 reverse biased detectivity, 374 RNEP, 374 saturation current, 149, 171, 172 signal-to-noise ratio, 375 spectral response, 86-90 structure, 144, 145 surface recombination velocity, 149 Piezoelectric phenomena, 259 Planck distribution, 322, 323 Plumbicon, 469 Polarization, spontaneous electric, 259 Power-spectraf-density, heterodyne signal, 382 Preparation techniques annealing, 118, 128-137, 142-144 cellular growth, I26 constitutional supercooling, 126-128 diffusion, 137-142 Hg,_,Cd,Te, 233-242 annealing, 240, 241 junction formation, 241, 242 melt growth, 234 purification of elements, 233, 234 vapor phase growth, 235-240 InSb, 63, 64 Pb,-,Sn,Se, 114-144 Pb,-,Sn,Te, 1 14-144 PV mode, see Photovoltaic detectors Pyroelectric detector, 259-285 detectivity, 270, 280, 281 electrical circuit, 263-266 electrode geometry, 283, 284 excess temperature, 262, 263 fabrication, 273-276 noise amplifier, 268, 269 Johnson, 268 radiation, 267
noise equivalent power, 268-272, 274 performance, 276-282 high-frequency, 278, 279 NEP, 276-280,284 response, 282 TGS performance, 265, 284, 285 thermal circuit, 261-263 thermal wave, 262, 263 propagation constant, 263 total energy mode, 273 voltage responsivity, 264-266 Pyroelectric materials, properties, 260, 266 Pyroelectric phenomena, 259 pyroelectric coefficient, 259, 260
Q Quantum efficiency diode detector, 145 internal photoeffect, InSb, 30, 33 mixer, 41 1, 421, 424 Pb,,Sn,Se, 155 Pb,_,Sn,Te diodes, 405 photovoltaic detector, 87-92 Si diodes, 486 Si monolithic arrays, 492 Quantum noise factor, 410,412-414 sensitivity limit, 422-424
R Radar energy detection, 400 heterodyne Doppler, 400 pulsed, 400 laser, 365, 4 W 0 3 configuration, 400 results, 400403 Radiation, environmental, 322 Radiation thermopiles, 287-3 18, see also Thermopiles arrays, 3 12-3 17 D* criterion, 301 design criteria, 299 detectivity, evaporated thermopiles, 311 device figure of merit, 299-301 Havens-limit thermal detector, 301, 302 M , criterion, 301, 302, 311
549
SUBJECT INDEX noise equivalent power, 3 11 properties profile, 302 responsivity, 296, 297 bulk thermopiles, 307 evaporated thermopiles, 309-3 11 time constant bulk thermopiles, 307 evaporated thermopiles, 3 11 Radiative recombination Hg,_,Cd,Te, 214-217 theory, 214 Rayleigh density function, 398-400 Readout methods, photodetector arrays charge storage mode (photon flux integration), 497, 499-504 effective gain, 501 illumination level, 501 excitation storage mode, 504 pattern recognition, 505 photocurrent mode, 497, 498 random access, 504, 505 Receiver (10.6 micron heterodyne) conversion gain, 411, 413, 421-425 design criteria, 414, 429-430 Ge (Cu doped), 415, 422-425 gigahertz frequency response, 413,414, 419, 422-424 NEP, 412, 422-425 summary of characteristics, 421-425 Receiver sensitivity, heterodyne detection, 412, 413, 422 Recombination, see also Carrier lifetime Hg,_,Cd,Te, 213-218 InSb, 35, 39, 43, 48, 54 Refractive index, InSb, 29-3 1 Response, see also Responsivity, spectral Hg,_,Cd,Te detectors PC, 249, 250 PV, 250, 251 pyroelectric detector, 265, 282 thermal detectors, 302-304 Response speed, 5, see also Response time PbSn chalcogenide detector, 161-163 radiation thermopiles, 3 11 Response time, 7, 8, see also Response speed compensated Ge:Hg, 426, 427 PC,41, 47,54, 59 Hg,-,Cd,Te, 226
PEM, 47, 59 uncompensated Ge:Cu, 426, 427 Responsivity spectral, 43, see also Voltage responsivity Ge:Cu, 342 InSb detectors, 72-77 PC, 45-57 PEM, 60,61 lead-tin chalcogenide detectors, 154-158, 165, 169-171 measurement, 341 Pb,_,Sn,Se diode, 384, 406 P C mode, 220, 221 photoconductors vs photodiodes, 405 PV mode, 228-230 voltage, 264, see also Pyroelectnc detectors radiation thermopiles, 3 11 Retrieval efficiency, 446-448 bandwidth variation, 447, 448 critical value junction diode, 447 photoconductor, 447 photomultiplier, 447 RNEP, see also Noise equivalent power, Real noise equivalent power p-n junction, reverse-biased, 374 photovoltaic detector, 374 Roll-over frequency, see Frequency response Rough-target heterodyning, see Diffuse reflector
S Scanning circuits, 494, 508 integration, 508 thin-film, 494 Scattered radiation heterodyning, see Diffuse reflector Scattering wheel, 375 Screening, free carrier, 439 Seebeck coefficient, 290 Sensitivity, see Noise equivalent power, Responsivity Sensitizing techniques, 9 Shockley-Read recombination, 39, 41 Hgl..,Cd,Te, 217, 218, 222, 223 InSb, 48, 50, 54
550
SUBJECT INDEX
Sicon, 469 Signal-to-noise ratio coherent detection, 372 heterodyne detector, 348 Ge:Cu, 380, 381 Pb,,Sn,Se, 386-388 IF output, 430 MBPD, 436 measurement, 375-378 photoconductor extrinsic, 375 versus photodiodes, 403, 404 photodiode (reverse biased), 373 photoemitter, 373 photovoltaic diode, 375 quantum theory, 372 shot noise limit, 447 Silicon absorption coefficient, 93 Al-doped, heterodyne detection, 415, 484 Au-doped, 478 detectors, 9 D:, 10, 492 MBPD, 448-450 p-n junction, 484, 485 quantum efficiency, 480, 486, 492 spectral response, 480, 485 Solid solutions, 111-Vcompounds, 96, 97 Solubility, see also Solid solutions substitutional alloys, 95-97 Spectral cutoff, 8 Spectral detectivity, see also D: InSb, 46, 51, 53, 56 PC detectors, 46, 51, 53, 56 PEM, 61,62 Spectral response, 6-8, 42 InSb, 40, 73 p-n junction devices, 86 Spectral responsivity, see Responsivity, spectral Speed of response, 5, see also Response speed Stationarity, 368 Stefan-Eoltzmann law, 322 Strontium-barium niobate heterodyne detection, 383 special materials, 383 pyroelectric detectors, 285
T Target motion, see Diffuse reflector Temperature, operating, photoconductors versus photodiodes, 405, 406 Temperature noise, 5 , see also Noise TGS, see also Triglycine sulfate, Pyroelectric detector heterodyne detection, 383 properties, 260 transmission, 275 Thallium sulfide (TI.$,), detectors, 9 Thermal conductivity CdTe, 187 Hg,-zCd,Te, 187 HgTe, 187 Thermal detectors, 7, 8, 260 bolometer, 8 D*, 8 Golay, 8 pyroelectric, 8 time constant, 8 Thermal expansion CdTe, 187 HgTe, 187, 188 Thermal wave, 262, see also Pyroelectric detector Thermoelectric materials, 297, 298 figure of merit, 297 Wiedemann-Franz ratio, 297, 300 Thermopiles, see also Radiation thermopiles design criteria, 299 history, 287-289 materials criteria, 297, 298 figure of merit, 297 radiation detectors, 287-3 18 responsivity, 296, 297 theoretical background, 289-297 heat balance, 292-296 Peltier coefficient, 290, 291 Seebeck coefficient, 290 Thomson coefficient, 29 I , 292 Thin-film transistor, 494 Thomson coefficient, 291, 292 Time constant, see Frequency response Time sequential information retrieval, see Readout methods, Photodetector arrays Tin oxide (SnO,), 478, 526
551
SUBJECT INDEX
Total energy detector, 272, 273 Transmission, see Optical transmission Triglycine sulfate, 260, 274, 275, see also TGS Tuning techniques, NBSFD compositional, 93 junction depth, 94 reverse biasing, 94 temperature, 93
U Uncertainty principle, 37 1
Vidicon, 470, 471 Voltage responsivity, 146 diode detector, 146
W Wavelength units, energy gap, 176 Wide-band detectors, 349, see also Broad band systems Wiedemann-Franz law, 297 Wien displacement Iaw, 322 Windows, IR transmission, 248
V van Cittert-Zernike theorem, 377 Vapor growth technique 116-1 19 Pb,-,Sn,Se, Pb,-,Sn,Te, 116-1 19
Z
Zinc sulfide (ZnS), 508, 524 Zinc telluride (ZnTe) band structure, 194-195
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